ERRATA 


P.  167,  line  20,  ‘trajectors’  should  be  ‘trajectories’. 

P.  167,  line  22,  ‘sight’  should  be  ‘site’. 

P.  173,  line  22,  ‘sight’  should  be  ‘right’. 

P.  175,  line  7,  ‘work’  should  be  ‘word’. 

P.  178,  line  9,  n = 100/20  = 5,  should  be  n = 200/20  = 10. 

P.  182,  line  30,  G^T,  should  be  G.T.. 

P.  204,  line  3,  abd  should  be  adb. 

P.  206,  line  21,  4,  7,  9,  should  be  .4,  .7,  .9. 

P.  208,  line  1,  200  should  be  1200. 

P.  215,  line  18,  ‘sight’  should  be  ‘site’. 

P.  226,  line  6,  2 yds.  should  be  .2  yds. 

P.  234,  line  4,  should  be = — =40. 

o o 

P.  237,  line  27,  ‘corrector’  should  be  ‘correction’. 

P.  272,  line  22,  GiT  should  be  G'T.  (Trajectory  G'T  omitted 
from  cut.) 

P.  272,  line  24,  Gi  should  be  G'. 

P.  273,  line  10,  Gi  T should  be  G'  T. 


rPORGE  WASHINGTON  ITOWERS 
“memorial  COETECTION 


duke  UNIVERSITY  LIBRARY 

DURHAM,  N.  C. 


presented  by 
•w.  w.  FLOWERS 


GUNNERY 

An  Elementary  Treatise 


INCLUDING  A GRAPHICAL  EXPOSITION 
OF  FIELD  ARTILLERY  FIRE 


BY 

JENNINGS  C.  WISE,  B.  S. 

Captain  and  Adjutant  First  Battalion  Field  Artillery,  Virginia  Volunteers 
(Formerly  Second  Lieutenant  U.  S.  Army) 


RICHMOND,  VA. 

B.  F.  JOHNSON  PUBLISHING  COMPANY 

1912 


Copyright  1912 

B.  F.  JOHNSON  PUBLISHING  COMPANY 
Entered  at  Stationers  Hall 
London,  England 

All  rights  reserved  for  all  countries 


ijlf  ("S  '-I- 


6^3./ 

V\l  il  ^ 


RESPECTFULLY  DEDICATED 

TO 

BRIGADIER  GENERAL  WILLIAM  WILSON  SALE 
Adjutant  General,  State  of  Virginia 


-50278 


Digitized  by  the  Internet  Archive 
in  2016  with  funding  from 
Duke  University  Libraries 


https://archive.org/details/gunnery01  wise 


CONTENTS 


PART  I— ELEMENTARY  COURSE  OF  MATHEMATICS 

Chapter  Page 

I Definitions  and  Use  of  Mathematical  Terms 3 

II  Common  Fractions 7 

III  Decimal  Fractions 12 

IV  Tables  of  Measure 17 

V Denominate  Numbers  23 

VI  Ratio  and  Proportion 27 

VII  Percentage  29 

VIII  Powers  and  Roots 31 

IX  Geometrical  Magnitudes  34 

X Mensuration  43 

XI  Algebraic  Expressions  and  Simple  Equations  ....  50 

PART  II— GUNPOWDER  AND  HIGH  EXPLOSIVES 

I Combustion,  Explosion,  Detonation 61 

II  Explosive  Mixtures — Gunpowder  68 

HI  Gunpowder — Continued  73 

IV  Smokeless  Powders  77 

V Explosive  Compounds — Guncotton  and  Nitroglycerin  . 81 

VI  Guncotton  Powders.  Dynamite.  Detonators  ....  90 

PART  III— BALLISTICS 

I Ballistics 99 

II  Interior  Ballistics  109 

III  Exterior  Ballistics 117 

PART  IV— SHRAPNEL  139 

PART  V— PRACTICAL  GUNNERY 

I Fire  and  Fire  Data 149 

II  Indirect  fire  and  Deflection 171 

III  Range  and  Ranging 209 

IV  Angle  of  Site 224 

V Corrector 230 

VI  Observation  of  Fire 239 

VII  Position  and  the  Mask 245 


PREFACE 


The  author  of  this  work,  if  it  may  be  so  styled,  desires  to 
explain  its  origin  and  its  purpose. 

With  the  idea  of  encouraging  his  officers  to  study,  the 
Commanding  Officer  of  the  First  Battalion  Field  Artillery, 
Virginia  Volunteers,  established  a central  school  for  the  offi- 
cers of  the  Battalion,  the  three  batteries  of  which  are  stationed 
in  Richmond,  Norfolk,  and  Portsmouth,  respectively.  Instruc- 
tion by  correspondence  was,  therefore,  necessary. 

The  first  year’s  course,  which  extended  from  January  to 
June,  1911,  embraced  Algebra,  Drill  Regulations,  Fire  Data, 
Hippology,  Military  Topography,  Military  Field  Engineering, 
and  3-inch  Material,  suitable  textbooks  being  obtained  from 
the  War  Department.  Upon  the  completion  of  this  course 
of  study,  it  was  decided  to  continue  the  school  for  another 
year  and  to  give  particular  attention  to  the  subject  of 
fire.  It  was  thought  that  a knowledge  of  Ballistics  and 
Explosives,  however  elementary,  would  be  of  great  value 
to  the  student  officers,  but  it  was  found  that  the  available 
works  on  these  subjects  were  too  advanced  for  those  who 
lacked  a technical  education.  As  Chief  Instructor  of  the 
school,  the  writer  then  set  about  the  preparation  of  a series 
of  lectures,  so  elementary  as  to  be  within  the  grasp  of  all, 
and  with  the  idea  of  explaining  the  reason  why  “for  every 
rule.”  For  the  sake  of  convenience  only,  these  lectures 
were  united.  A technical  treatise  was  never  contemplated, 
nor  has  a full  and  logical  treatment  of  the  subjects  touched 
upon  been  attempted.  These  lectures  are  but  a series  of 
notes  which  it  is  hoped  may  assist  in  the  study  of  the  many 

vii 


PREFACE 


viii 

excellent  textbooks  to  be  had.  Certain  other  information 
has  been  included  which  it  was  thought  would  prove  of  interest 
and  benefit  to  the  officers  of  the  school. 

That  part  of  the  introduction  entitled  “Study  and  the  Value 
of  Theory”  was  inserted  at  the  very  beginning  of  the  book 
in  the  hope  that  the  admonitions  of  the  great  soldiers  therein 
set  forth  might  arrest  the  attention  and  at  once  arouse  the 
interest  of  officers  inclined  to  look  with  impatience  upon 
all  forms  of  professional  theory.  It  was  thought  that  such 
officers  would  at  least  be  inspired  to  exercise  greater  diligence 
in  the  study  of  the  fundamental  principles  of  their  own  branch 
of  the  service. 

If  the  author  has  here  and  there  entered  upon  the  field  of 
tactics,  he  must  be  pardoned,  for  it  has  only  been  done  to 
emphasize  technical  points  which  tactical  considerations 
frequently  involve. 

No  claim  to  originality  is  asserted  by  the  writer,  except  as 
to  the  arrangement  of  the  book  and  the  method  of  gradual 
development  of  the  subjects  treated,  and  the  graphic  solu- 
tion of  problems  which  in  other  forms  appear  unduly  difficult 
to  the  novice.  The  text  of  the  drill  regulations  has  been 
closely  followed  in  several  instances  at  some  length,  because 
there  was  nothing  in  the  particular  passages  requiring  elabo- 
ration, and  it  was  necessary  to  include  them  in  order  to  pre- 
serve the  continuity  of  the  discussion.  The  writer  has  not 
hesitated  to  use  verbatim  the  best  he  could  find  from  the  fol- 
lowing sources,  which  should  be  consulted  by  the  ambitious 
artillery  student: 

The  Field  Artillery  Journal;  The  Infantry  Journal;  War 
Department  Reports  on  Shrapnel  Fire;  Modern  Guns  and 
Gunnery,  Bethell;  Ballistics,  Hamilton;  Interior  Ballistics, 
Ingalls;  Ordnance  and  Gunnery,  Lissak;  Ordnance  and  Gun- 
nery, Metcalf;  Ordnance  and  Gunnery,  Bigelow;  Ordnance 
and  Gunnery,  Bruff;  Military  Explosives,  Weaver;  A^rtillery 
Circular  B,  1902,  Walke;  Artillery  Circular  H,  1893,  Bhss; 


PREFACE 


IX 


Gunnery  and  Explosives,  Westervelt;  Handbook  for  Light 
Artillery,  Dyer;  Handbook  for  3-inch  Material;  Artillery 
Drill  Regulations;  Field  Service  Regulations;  Weldon  Range 
Finder,  Pamphlet,  War  Department;  Applied  Principles  of 
Field  Fortifications,  Woodruff;  Mditary  Field  Engineering, 
Beach;  Notes  on  Field  Artillery,  Spaulding;  Field  Artillery 
with  the  Other  Arms,  May;  The  Tactical  Handling  of  Q.  F. 
Field  Artillery,  Roquerol;  Selected  Translations  Pertaining 
to  Boer  War,  War  Dept,;  German  Official  Account  of  the 
War  in  South  Africa;  U.  S.  Official  Reports  of  the  Boer  War; 
U.  S.  Official  Reports  of  the  Russo-Japanese  War;  A Staff 
Officer’s  Scrap  Book,  Hamilton;  Mihtary  Memoirs  of  a 
Confederate,  Alexander;  The  Science  of  War,  Henderson; 
Various  Accounts  of  the  Franco-Prussian  War. 

Jennings  C.  Wise, 

Captain  and  Adjutant, 

1st  Batt.  F.  A.  Va.  Vols. 


Richmond,  Virginia, 
Feb.  29,  1912. 


INTRODUCTION 


STUDY  AND  THE  VALUE  OF  THEORY 

“Success  in  war  is  almost  wholly  in  the  hands  of  the  officers. 
There  have  been  soldiers’  battles,  in  which  the  valor  of  the 
man  has  redeemed  the  blunders  of  the  general,  but,  as  has 
been  truly  observed,  there  has  never  been  a soldiers’  cam- 
paign. Even  the  most  enthusiastic  patriots  must  be  led; 
and  an  army  of  stags,  says  the  adage,  commanded  by  a lion, 
is  better  than  an  army  of  lions  commanded  by  a stag.”  Thus 
has  Henderson  truly  written. 

In  consequence  of  this  truism,  on  every  hand  we  hear  the 
young  officer,  especially  the  volunteer,  despairingly  inquire 
how  may  he  prepare  to  honorably  acquit  himself  of  the  obli- 
gations which  war  will  impose  upon  him.  He  is  appalled 
by  the  increasing  demands  of  the  military  profession  and,  in 
proportion  to  his  earnestness,  alarmed  by  an  appreciation 
of  his  own  ignorance.  “I  desire  to  do  all  in  my  power,” 
says  he,  “but  know  not  what  to  do  to  prove  a lion  rather 
than  a stag  should  the  role  of  a leader  become  my  part.” 

While  the  following  argument  is  adapted  to  the  artillery 
officer,  it  being  presupposed  that  this  paper  will  find  readers 
in  that  branch  of  the  service  upon  which  the  greatest  demand 
is  now  being  made  by  reason  of  the  radical  developments  in 
the  science  of  gunnery,  yet  the  appeal  is  general.  It  is 
believed,  however,  that  in  no  other  branch  of  the  service 
will  the  value  of  theory  be  more  easily  perceived  than  in 
the  artillery. 

To  Wellington  is  attributed  that  oft-repeated  remark: 


XI 


INTRODUCTION 


xii 

‘‘Waterloo  was  won  on  the  playgrounds  of  Rugby.”  I 
seriously  doubt  if  such  a remark  were  ever  made  by  one,  wno, 
like  Wolfe,  was  one  of  the  most  zealous  students  of  his  time, 
any  more  than  Lee  ever  claimed  the  superiority  of  the  Army 
of  Northern  Virginia  over  its  antagonists  during  the  first 
years  of  the  war  to  have  been  due  to  the  thoroughbred  horse 
and  the  shooting  dog  of  the  South.  Both  WeUington  and  Lee 
recalled  too  often  the  hours  they  had  devoted  to  professional 
study;  both  too  frequently  witnessed  the  blunders  of  gallant 
but  ignorant  men,  to  attribute  victory  to  courage  and  physi- 
cal training  alone. 

The  repetition  of  this  supposed  saying,  unqualified  as  it 
is,  of  so  great  a soldier  as  Wellington,  has  perhaps  done  more 
harm  than  good,  for  thereby  the  thoughtless  are  only  con- 
firmed in  the  belief  that  great  generals  are  lurking  upon  every 
playground  and  will  emerge  from  obscurity  in  the  hour  of 
need.  Thus  is  the  world  misled,  and  in  the  pursuit  of  such 
a phantasy  does  our  own  country  lead.  The  fact  that  untu- 
tored soldiers  have  met  with  miraculous  successes  renders 
impatient  the  average  citizen  with  all  but  the  unprofessional. 
If  only  the  brilliant  aphorisms  of  General  “Dick”  Taylor 
could  strike  the  popular  conscience  with  full  force  innumer- 
able disasters  would  be  averted.  The  very  title  of  his  book, 
itself  a most  valuable  contribution  to  unprejudiced  history, 
is  suggestive  of  our  military  policy — “Destruction  and  Recon- 
struction.” But  I cannot  refrain  from  quoting  a passage 
therefrom  which  contains  in  a few  words  what  nations  have 
failed  to  grasp  through  centuries  of  experience. 

“Although  since  the  days  of  Nimrod  war  has  been  the  con- 
stant occupation  of  men,  the  fingers  of  one  hand  suffice  to 
number  the  great  commanders.  The  ‘unlearned’  hardly 
think  of  usurping  Tyndall’s  place  in  the  lecture  room,  or  of 
taking  his  cuneiform  bricks  from  Rawlinson,  yet  the  world 
has  been  much  more  prolific  of  learned  scientists  and  phil- 
ologers^than  of  able  generals.  Notwithstanding,  the  average 


STUDY  AND  THE  VALUE  OF  THEORY 


xiii 


American  . . . would  not  have  hesitated  to  supersede 

Napoleon  at  Austerhtz  or  Nelson  at  Trafalgar.  True,  Cleon 
captm’ed  the  Spartan  garrison,  and  Narses  gained  victories, 
and  Bunyan  wrote  the  ‘Pilgrim’s  Progress,’  but  pestilent  dema- 
gogues and  mutilated  guardians  of  Eastern  zenanas  have  not 
always  been  successful  in  war,  nor  the  great  and  useful  pro- 
fession of  tinkers  written  allegory.” 

It  may  be  added  that,  while  all  thoroughbreds  do  not  make 
race  horses,  yet  we  are  not  justified  thereby  in  entering 
percherons  in  a great  event. 

The  fact,  however,  that  the  lessons  of  the  great  conflict  of 
1861-5  will  be  forgotten  before  the  advent  of  another  war, 
and  that  the  professional  soldier  will  be  discredited  at  first 
to  the  great  loss  of  a people  misled  by  conceit,  does  not  relieve 
him  from  the  obligations  of  his  calling.  Nor  do  I mean  to 
suggest  that  the  professional  is  necessarily  educated  and 
worthy  of  high  command.  The  mere  fact  that  he  has  bloomed 
forth  from  a cadet  to  a subaltern  of  the  line  does  not  imply 
that  he  will  imbibe  the  principles  which  constitute  the  science 
of  war  and  develop  the  qualities  of  a leader.  Until  recently 
it  would  seem  our  youthful  soldiers  were  expected  to  absorb 
military  experience  from  the  air  of  the  Hudson.  While  the 
course  of  mathematics  and  physical  training  through  which 
they  passed  was  most  excellent,  it  was  preposterous  to  suppose 
that  the  youth  could  acquire  along  with  a technical  education 
any  more  than  a foundation  of  abihty  for  future  command. 
How  ludicrous  must  have  appeared  the  mere  graduate  of 
our  Academy  to  the  highly  cultured  officers  of  the  foreign 
staff  colleges!  But  with  our  general  staff  has  come  a con- 
ception that  West  Point  alone  cannot  make  generals, 
however  valuable  its  system  may  be  in  weeding  out  unsuit- 
able material. 

Riichel  said  the  soul  of  the  Prussian  Army  was  in  its  offi- 
cers. That  the  spirit  of  the  corps  of  officers  bespeaks  the 
spirit  of  the  whole  army  is  claimed  by  Von  der  Goltz  to  be 


XIV 


INTRODUCTION 


but  a repetition  of  what  is  universally  observed  in  political 
life.  “ So  long/’  says  he,  “as  the  educated,  the  leading, 
classes  maintain  their  efficiency,  the  people  also  will  be  stout 
and  capable.”  And  again  he  asserts  that  especial  value 
must  be  laid  upon  education,  because  it  is  the  basis  of  noble 
and  moral  qualities. 

Frederick,  Napoleon,  Clausewitz,  Von  der  Goltz,  Wolseley, 
and  many  others  have  attempted  to  analyze  the  composition 
of  a great  general,  education  in  each  estimate  being  cited 
as  an  important  element,  and  though  Timur  and  Onosander 
did  not  use  the  word,  the  requisite  attributes  enumerated  by 
them  can  only  spring  from  the  loin  of  knowledge.  Lord 
Roberts  reminds  us  that  even  self-reliance,  that  cardinal 
requisite  of  a successful  general,  can  only  come  from  the  most 
careful  education.  Therefore,  it  would  seem  it  is  not  to  be 
expected  that  men  devoid  of  military  knowledge  and  experi- 
ence, however  courageous  and  patriotic  they  may  be,  will 
develop  into  successful  leaders  on  the  battle  field. 

The  tendency,  or  perhaps  I should  say  the  habit,  of  the 
uneducated  soldier,  as  well  as  of  the  citizen,  has  ever  been  to 
minimize  the  importance  of  theoretical  work.  It  is  too 
common  that  we  hear  him  scoff  at  “paper  war.”  He  pre- 
fers to  lay  aside  the  pen  while  the  blade  rusts  idle  in  the 
scabbard.  But  it  has  been  my  observation  that  such  indiffer- 
ence is  due  more  to  ignorance  than  to  conviction,  and  that 
with  the  dawning  of  the  military  light  the  true  value  of 
theory  is  seen. 

This  is  true.  A man  could  not  make  an  intelligent  survey 
in  the  field  unless  he  had  been  trained  in  the  theory  of  his 
instruments.  Neither  can  the  officer  who  has  never  had  the 
experience  of  actual  campaign  hope  to  acquire  a practical 
knowledge  by  groping  in  the  dark.  There  is  no  place  for  the 
military  empiric  to-day.  Indeed,  the  lessons  of  actual  warfare 
are  not  digestible  to  those  who  lack  the  saliva  of  theory — 
they  are  negative  rather  than  positive. 


STUDY  AND  THE  VALUE  OF  THEORY 


XV 


“ In  all  ages  the  power  of  intellect  has  asserted  itself  in 
war.  It  was  not  courage  and  experience  only  that  made 
Hannibal,  Alexander,  and  Caesar  the  greatest  names  of  antiq- 
uity. Napoleon,  Welhngton,  and  the  Archduke  Charles 
were  certainly  the  best  educated  soldiers  of  their  time;  while 
Lee,  Jackson,  and  Sherman  probably  knew  more  of  war 
before  they  made  it  than  anyone  else  in  the  United  States.” 
The  fact  that  the  training  of  some  successful  leaders,  for 
instance,  Cromwell,  Marlborough,  Clive,  Nelson,  Grant, 
and  Forrest,  was  altogether  practical  is  but  the  exception 
proving  the  rule  that  most  great  soldiers  are  deep  students 
of  war. 

Frederick  the  Great,  in  speaking  of  officers  who  relied  on 
their  practical  experience  alone,  caustically  remarked  that  there 
were  in  the  army  two  commissariat  mules  which  had  served 
through  twenty  campaigns,  “but,”  he  added  significantly, 
“they  are  mules  still.” 

Von  der  Goltz  states  that  illustrious  soldiers  always  become 
more  clear-sighted  and  resourceful  in  moments  of  the  greatest 
danger,  while  around  them  all  are  working  with  blunted 
senses.  He  then  goes  on  to  discuss  courage,  a divine  courage, 
as  that  which  clears  the  mind  at  such  a time.  But  to  what 
end  would  the  mind  be  taxed  if  the  mental  armory  were  not 
well  stored  with  military  resourcesf  The  dispatches  of  Napo- 
leon, of  Wellington,  and  of  Moltke  are  sufficient  proof  that 
they  depended  upon  hard  thinking  and  calculations,  rather 
than  upon  a God-given  courage  or  upon  the  principle  of 
stat  pro  ratione  voluntas  which  we  are  so  fond  of  associating 
with  genius. 

“If  I were  asked  to  put  my  finger  on  the  most  important 
lesson  that  may  be  learned  from  the  past,  I should  reply,” 
says  Henderson,  “that  history  teaches  us  that  courage, 
numbers,  armament,  and  entrenchments  are  of  no  avail  if 
the  troops  are  badly  led.  ...” 

Some  men,  in  fact  a majority  of  men,  are  by  nature  so  con- 


XVI 


INTRODUCTION 


stituted  as  to  render  them  unsuited  to  command.  Such 
men,  while  they  will  not  be  developed  into  leaders  by  study, 
will  be  greatly  improved. 

Theory,  applied  to  the  profession  of  arms,  is  to  some  an 
obnoxious  word,  but  only  to  those  who  disdain  the  advice 
of  Napoleon.  “It  is  not  pretended”  says  McDougall, 
“that  study  will  make  a dull  man  brilliant,  nor  confer  reso- 
lution and  rapid  decision  on  one  who  is  timid  and  irresolute 
by  nature,  but  the  quick,  the  resolute,  the  daring,  deciding 
and  acting  rapidly,  as  is  their  natme,  will  be  all  the  more 
likely  to  decide  and  act  correctly  in  proportion  as  they  have 
studied  the  art  they  are  called  upon  to  practice.” 

One  who  studies  the  life  of  the  hero  of  St.  Vincent,  the  Nile, 
Copenhagen,  and  Trafalgar,  must  be  impressed  by  Nelson’s 
utter  lack  of  grasp  of  the  fundamental  principles  of  strategy 
in  the  earlier  years  of  his  career.  In  discussing  the  Admiral’s 
erroneous  views  as  to  Napoleon’s  impending  Italian  campaign, 
Mahan,  in  his  epochal  work,  says: 

“The  mistake,  if  mistake  it  was,  illustrates  aptly  the  errors 
into  which  a man  of  great  genius  for  war,  of  quick  insight, 
such  as  Nelson  indisputably  had,  can  faU,  from  want  of 
antecedent  study,  of  familiarity  with  those  leading  princi- 
ples, deduced  from  the  experience  of  the  past,  which  are  per- 
haps even  more  serviceable  in  warning  against  error  than  in 
prompting  to  right.” 

Who  shall  say  that  Nelson’s  early  career  would  not  have 
been  even  more  illustrious  had  he  been  a deep  student  of  war? 

“Without  character  and  capacity,  physical  and  moral 
courage,  coolness,  and  self-reliance,  it  is  impossible,”  says 
Henderson,  “that  a man  can  become  a great  soldier.”  “But,” 
he  adds,  “however  strong  he  may  be  in  the  possession  of  such 
qualities,  study  and  practice  can  never  be  anything  else  but 
beneficial.” 

One  of  our  most  distinguished  Confederate  generals,  re- 
ferring to  officers  not  exceptionally  gifted,  said:  “Conscientious 


STUDY  AND  THE  VALUE  OF  THEORY 


xvii 


study  will  not  perhaps  make  them  great,  but  it  will  make 
them  respectable;  and  when  responsibility  of  command  comes 
they  will  not  disgrace  their  flag,  injure  their  cause,  nor  murder 
their  men.” 

Military  science,  the  study  of  which  is  so  earnestly  advo- 
cated by  all  great  soldiers,  is  in  no  sense  an  arbitrary  code. 
On  the  contrary,  its  principles  are  the  essence  of  an  experi- 
ence which  the  student  but  acquires  second  hand.  The 
maxims  of  Napoleon  are  but  deductions  from  a practice  of 
which  he  was  the  most  successful  exponent.  The  genius  of 
Bonaparte  amplified  rather  than  blindly  followed  hitherto 
existing  rules  of  war. 

The  benefit  to  be  derived  from  the  study  of  the  military 
art  is  the  mastery  of  a theory  upon  which  the  soldier  may 
act  with  some  degree  of  confidence.  As  new  weapons  are 
evolved  or  old  ones  developed,  it  becomes  necessary  to  postu- 
late a theory  for  their  use,  which  it  may  not  always  be  possi- 
ble to  base  upon  actual  experience.  In  such  case  the  theory  is 
but  a mental  picture  gained  from  the  study  of  a map.  The 
traveler  may  find  practical  obstructions  in  his  way,  but  the 
short-cuts  will  enable  him  to  regain  his  course,  whereas  one 
insensible  of  the  general  direction  is  only  confused  by  the 
by-paths  which  might  have  subserved  his  convenience.  Which 
of  the  by-paths  we  find  in  practice  are  to  be  followed  can  only 
be  known  by  keeping  in  mind  our  general  trend.  Followed 
blindly,  as  practical  obstacles  arise,  these  routes  will  only 
serve  to  lead  us  astray.  There  is  no  time  in  actual  campaign 
to  explore  each  alley  of  the  maze — tentanda  via  est.  And  so 
it  is  certain  that  he  who  experiences  the  failure  of  a theory 
is  more  able  to  rectify  his  course  than  one  who  encounters 
difficulties  without  being  able  to  discern  the  false  turns  in 
the  road. 

It  is  true  that  theory  by  itself  will  avail  but  little.  Wfien 
he  was  asked  the  best  means  of  learning  the  art  of  war.  Lord 
Seaton,  a Peninsular  veteran,  replied:  “Fighting,  and  a d — d 


INTRODUCTION 


xviii 

deal  of  it.”  But  practical  experience  falls  to  the  lot  of  few, 
and  unless  it  forms  a basis  for  reflection,  and  is  amplified  by 
comparison  with  the  experience  of  others,  loses  half  its  value. 
Reflection  and  comparison  are  obviously  impossible  unless 
the  brain  has  been  trained  to  think,  and  the  mind  is  stored 
with  knowledge  of  the  past. 

The  Archduke  Charles  remarked  that  much  experience 
and  a passion  for  study  were  indispensable  requisites  to  form 
a great  captain.  “What  we  have  seen  with  our  own  eyes,” 
says  he,  “is  not  sufficient,  for  where  is  he  whose  life  has  been 
so  eventful  as  to  have  made  him  experienced  in  everything? 
He  can  only  become  an  able  general  who  adds  the  knowledge 
of  others  to  his  own;  who  appreciates  the  researches  of  those 
who  have  gone  before  him;  and  who  recurs  to  the  mihtary 
exploits  and  great  achievements  which  the  history  of  war 
supplies,  as  his  standard  of  comparison.” 

Thus  we  see  that  this  illustrious  soldier,  while  asserting 
the  necessity  of  practical  experience,  insists  upon  study  as 
a pre-requisite  to  leadership.  We  must  not  be  misled  by  an 
erroneous  construction  of  Napoleon’s  maxim,  which  says: 
“Commanders-in-chief  are  to  be  guided  by  their  own  experi- 
ence or  genius.  Tactics,  evolutions,  the  science  of  the  engineer 
and  the  artillery  officer  may  be  learned  from  treatises,  but 
generalship  is  acquired  only  by  experience,  and  the  study 
of  the  campaigns  of  all  great  captains.”  There  is  no  warrant 
to  underestimate  the  weight  accorded  the  element  of  study 
by  the  author  of  this  saying.  The  language  of  Napoleon 
and  the  Archduke  alike  enjoins  us  to  consider  practice  and 
theory  in  conjunction,  Lord  Seaton  notwithstanding. 

It  is  not  intended  to  disregard  that  essential  quality  of 
military  genius  which,  so  far,  has  never  been  defined;  that 
quality  which  Jackson  of  the  Valley  possessed  and  which 
Jackson  of  the  Peninsula,  lacked — that  indefinable  quality 
which  made  Jackson  the  hero  of  the  Shenandoah,  and  Hood  the 
failure  of  Spring  Hill.  No  conception  of  Jackson’s  mind 


STUDY  AND  THE  VALUE  OF  THEORY 


XIX 


could  have  been  more  masterly  than  Hood’s  execution  up 
to  the  moment  for  attack  at  Spring  Hill.  Had  his  orders 
even  then  been  obeyed  the  Confederacy  would  have  claimed 
another  genius,  and  the  bloody  disasters  of  the  Harpeth 
would  not  be  recorded  in  history.  My  point  is  that  the  plan 
is  but  the  theory — without  more  the  conception  is  valueless 
— and  it  is  that  illusive  something  bridging  over  with  a hair 
the  chasm  between  victory  and  failure  which  Jacksons 
possess  and  Hoods  lack.  In  the  distinction  the  question 
of  courage  plays  no  part.  Von  der  Goltz  has  only  in  part 
predicated  the  truth,  for  surely  Hood  was  not  braver  at 
Franklin  than  the  day  before,  nor  was  Jackson  of  Bull  Run 
lacking  in  courage  while  on  the  Chickahominy.  The  psycho- 
logical element  of  military  success  on  the  battlefield  cannot 
be  further  discussed  here.  It  is  merely  alluded  to  in  order 
that  the  writer’s  argument  in  favor  of  another  element  may 
not  be  said  to  ignore  psychology  in  war. 

That  theory  may  be  preconceived  as  well  as  retrospective 
in  character  is  also  true.  The  most  striking  example  of  the 
application  of  such  a theory  is  that  presented  by  the  French 
mind  and  pen.  Without  firing  a shot  the  logicians  of  France 
have  forced  upon  a reluctant  world,  somewhat  contemptuous 
after  Sedan,  the  recognition  of  the  fact  that  the  philosophy 
of  war  is  not  necessarily  forged  in  the  white  heat  of  battle. 
Without  firing  a shot  the  French  army  has  been  rehabilitated, 
and  little  has  been  borrowed  from  its  erstwhile  conqueror 
except  the  conception  of  military  brain  power,  of  which 
Moltke,  at  the  head  of  the  German  Great  General  Staff, 
was  an  illustrious  exponent. 

Less  than  twenty  years  ago,  not  only  the  present  type  of 
field  gun,  but  the  method  of  its  employment,  was  deduced 
by  General  Langlois  of  the  French  Army.  Looked  upon  at 
the  time  (1892)  as  chimerical,  the  theories  of  this  celebrated 
artillerist  took  form  about  1898.  Germany,  at  first  inclined 


XX 


INTRODUCTION 


to  make  light  of  the  whole  plan,  was  soon  won  over,  and  to-day 
the  rapid-fire  gun,  which  at  first  appeared  utterly  imprac- 
tical, awaits  a chance  to  demonstrate  its  power  in  the  hands 
of  the  modern  artillerist.  I say  awaits  its  chance  advisedly, 
for,  contrary  to  the  general  belief,  this  gun  has  not  yet  been 
tried  in  war,  if  we  believe  Brigadier-General  M.  M.  Macomb, 
U.  S.  Army,  who  was  present  in  the  capacity  of  a military 
observer  at  all  the  great  battles  of  the  Russo-Japanese  War 
and  clearly  distinguishes  the  field  guns  used  by  both  armies 
from  our  own  type  and  those  of  most  of  the  European  powers. 

But  in  spite  of  the  French  Revolution  in  the  science  of 
field  artillery  one  salient  feature  remains  the  same  as  before — 
the  final  test  of  artillery  efficiency,  the  ultimate  object  of 
the  artillery,  is  to  deliver  an  effective  and  timely  fire,  for  this 
is  the  only  arm  that  has  no  action  except  fire.  To  this  extent 
then  the  French  theory  is  not  preconceived. 

The  experiences  which  field  artillery  will  undergo  in  actual 
campaign  are  summed  up  by  General  Macomb  as  follows: — 

1 — Transportation. 

2.  — Camping. 

3. — Marching. 

4.  — Bivouacking. 

5.  — Occupation  of  position. 

6.  — Fire. 

And  the  greatest  of  all  these  is  fire.  No  amount  of  tactical 
knowledge  on  the  part  of  the  officers,  no  excellence  in  march- 
ing, camping,  scouting,  reconnoitering,  etc.,  no  perfection  in 
artillery  duties  up  to  the  time  of  opening  fire,  is  of  any  use 
whatever,  if  the  battery  cannot  hit;  in  such  case  artillery 
becomes  “telum  imbelle,  sine  ictu” 

Fire  then  is  the  ultimate  end  of  field  artillery;  it  is  the  only 
reason  for  its  existence;  if  ineffective  in  fire,  it  has  no  title 
to  respect. 

“There  is  a school  of  writers  wRo  claim  that  the  efficiency 
of  modern  weapons  is  but  little  greater  than  that  of  the  older 


STUDY  AND  THE  VALUE  OF  THEORY 


XXI 


ones,  due  to  the  fact  that  every  weapon  must  be  operated 
by  a man,  and  that  men,  as  fighters,  have  deteriorated  with 
the  progress  of  civihzation,  in  almost  the  same  degree  that 
weapons  have  improved — that,  under  the  best  of  circumstances, 
men  get  as  much  excited,  and  just  as  much  demoralized, 
as  ever;  that  these  emotions  manifest  themselves  in  dimness 
of  eyesight,  trembling  of  the  hands,  oblivion  to  surroundings, 
neglect  of  details,  etc.,  etc.”  There  may  be  a good  deal 
of  truth  in  this.  The  greater  the  extent  to  which  it  is  true 
the  greater  the  necessity  for  every  man  in  the  artillery,  the 
weapon  of  which  is  the  most  intricate  of  all,  to  become  so 
accustomed  to  the  performance  of  his  duties  that  he  will 
do  his  part  as  a matter  of  habit.  The  effectiveness  of  our 
fire  depends  upon  the  turn  of  numberless  cranks.  However 
accurate  all  others  may  be,  if  one  single  man  neglects  his 
turn  the  shot  goes  wild.  And  who  of  us  wishes  to  fail  at  the 
critical  moment  so  long  expected  and  so  long  and  earnestly 
prepared  for  at  the  expense  of  millions  of  treasure?  Think 
of  the  mortification  which  would  come  to  us  should  we  encoun- 
ter the  reproachful  gaze  of  a gallant  and  shattered  infantry! 
Failure  in  peace  is  a bitter  portion — failure  in  war  is  worse 
by  the  number  of  lives  it  costs.  And  so  the  artillerist  must 
study;  he  must  familiarize  himself  with  every  turn  of  the  crank, 
so  that  failure,  if  it  must  come,  will  be  due  to  the  crank  and 
not  to  the  negligent  ignorance  of  the  operator. 

Every  nation  has  either  evolved  a doctrine  of  war  or  adopted 
the  conception  of  another.  Whether  it  be  French  or  German 
in  spirit,  adhered  to  by  the  British  and  the  Japanese  respec- 
tively, its  doctrine  is  that  which  gives  to  an  army  the  energy 
of  definite  motion.  Without  a conception  of  war  the  bravest 
army  is  inert  and,  like  that  of  Kuropatkin,  its  striking  power 
is  worn  away  in  useless  friction. 

The  spirit  of  the  doctrine  must  permeate  every  unit — 
■ — nay  more — every  breast,  and  that  of  the  Field  Ai’tillery 
must  be: 


xxn 


INTRODUCTION 


Co-ordination  of  men,  horses,  and  material  by  industry 
and  care; 

Attention  to  detail,  unselfish  co-operation,  unswerving 
obedience  without  fear  of  responsibility; 

Strong  initative,  careful  consideration,  prompt  decision,  and 
celerity  of  execution.  From  these  an  effective  fire  will  result. 

Just  as  there  is  a tendency  on  the  part  of  the  ignorant  to 
decry  theory,  so  there  is  danger  of  the  military  bookworm 
becoming  fettered  by  formulae.  This  extremity  is,  of  conrse, 
as  pernicious  as  the  other.  “I  hope,”  says  Lord  Wolseley, 
‘‘the  officers  of  her  Majesty’s  Army  may  never  degenerate 
into  bookworms.  ...  At  the  same  time,  all  now  recog- 
nize that  the  officer  who  has  not  studied  war  as  an  applied 
science;  who  is  ignorant  of  modern  military  history,  is  of 
little  use  beyond  the  rank  of  Captain.  . . . Experi- 

ence enables  me  to  warn  all  these  determined  men  of  how 
small  their  chance  is  of  ever  reaching  any  great  position  in 
the  army  unless  they  devote  many  of  their  spare  hours  every 
week  to  a close  study  of  tactics  and  strategy  as  dealt  with 
in  the  best  books  upon  recent  wars.” 

It  is  a mistake,  I believe,  for  the  student,  even  though 
he  be  a citizen  soldier,  to  conclude  that  the  practical  science 
of  field  artillery,  at  least,  has  become  so  thoroughly  formu- 
lated as  to  leave  no  room  for  the  brilliant  originahty  of  what 
we  call  military  genius.  The  zest  with  which  the  good  volun- 
teer officer  undertakes  his  duty  is  in  itself  sufficient  to  ensure 
the  rapid  mastery  of  his  duties  and  an  efficiency  which  will 
equal,  and  possibly  at  times  excel,  that  of  the  professional 
grown  old  in  the  service,  for  the  stranger  often  detects  that 
in  our  midst  which  we  ourselves  have  not  seen.  With  work 
which  is  a half-pastime,  wherein  they  find  relief  from  the  rou- 
tine of  their  ordinary  avocations,  monotony  has  no  place. 
The  very  freshness  of  their  obligations  is  attractive  of  zeal 
and  industry. 


STUDY  AND  THE  VALUE  OF  THEORY  xxiii 

With  each  advance  in  the  art  of  war,  somebody  must 
practically  demonstrate  the  proper  usage  under  the  innova- 
tion; here  comes  into  play  the  mental  enthusiasm  of  the  volun- 
teer which  gave  to  Europe  a new  system  of  artillery  tactics 
in  1861-5,  along  with  many  other  developments  in  the  art 
of  war.  The  writer  is  happy  in  the  feeling  that  the  unbending 
tenacity  of  Pendleton,  of  Long,  of  Lindsay  Walker,  of  Carter, 
of  Poague  and  the  brilliant  initiative  of  Alexander,  of  Pegram,  of 
Pelham,  of  Haskell,  of  Latimer,  of  Bearing,  and  of  Chew,  which 
together  constituted  a creative  force,  will  prove  of  even  more 
practical  value  in  the  application  of  modern  tactics  than 
in  the  past.  Why  should  this  not  be  so?  The  modern  weapon 
is  of  such  infinite  superiority  to  that  of  the  60’s  that  the 
impress  of  genius  must  be  the  more  keenly  felt.  We  must 
not  rely  upon  genius,  however,  but  upon  the  man-made 
rather  than  the  God-given  leader. 

At  the  close  of  this  somewhat  random  dissertation  on  the 
value  and  the  necessity  of  theory,  let  me,  therefore,  recommend 
the  advice  which  Sir  Charles  Napier,  a military  genius  him- 
self, who  did  not  disdain  to  study  his  profession,  but  thought 
it  indispensable  to  success,  gave  a young  officer: 

“By  reading  you  will  be  distinguished;  without  it,  abilities 
are  of  little  use.  A man  cannot  learn  his  profession  without 
constant  study  to  prepare  especially  for  the  higher  ranks. 
When  in  a post  of  responsibility  he  has  no  time  to  read; 
and  if  he  comes  to  such  a post  with  an  empty  skull  it  is 
then  too  late  to  fill  it.  Thus  many  people  fail  to  distinguish 
themselves,  and  say  they  are  unfortunate,  which  is  untrue; 
their  own  previous  idleness  unfitted  them  to  profit  by  fortune.” 

And  if  there  still  remain  any  doubt  in  the  young  officer’s 
mind  as  to  the  way  to  fit  himself  for  command,  let  him  ponder 
the  encouraging  advice  of  the  greatest  genuis  war  has  produced. 
Said  Napoleon:  “Read  over  and  over  again  the  campaigns 
of  Alexander,  Hannibal,  Csesar,  Gustavus,  Turenne,  Eugene, 
and  Frederick.  Make  them  your  models.  This  is  the  only 


XXIV 


INTRODUCTION 


way  to  become  a great  general,  and  to  master  the  secrets 
of  the  art  of  war.  Your  genius,  when  enhghtened  by  this 
study,  will  induce  you  to  reject  such  maxims  as  conflict  with 
the  principles  of  those  great  commanders.” 

The  lesson  which  it  has  been  attempted  to  impress  upon 
the  mind  of  the  young  officer  in  the  foregoing  pages  is,  whether 
he  be  lieutenant  or  of  higher  degree,  let  him  not  rust  his 
mental  faculties,  for  in  peace  the  textbook  and  the  pen 
must  serve  as  the  military  lubricant.  But  study  to  be  of 
beneflt  must  be  systematic,  and  further,  it  must  not  be  mere 
drudgery.  Without  system,  the  labor  of  study  multiplies 
itself  and  dulls  our  interest.  The  most  zealous  student  must 
feel  that  his  efforts  are  being  rewarded,  and  for  this  reason 
intellectual  culture  must  be  accompanied  by  mental  enjoy- 
ment. The  writer,  therefore,  makes  bold  to  supplement 
the  advice  of  the  great  leaders  which  he  has  embodied  herein 
by  appending  a course  of  military  study,  elementary,  yet 
progressive,  for  the  repetition  of  such  advice  without  guidance 
is  more  or  less  superficial. 

It  is  not  pretended  that  the  authorities  cited  are  the 
best  from  every  viewpoint,  yet  it  is  asserted  with  some 
degree  of  confidence,  based  upon  an  intimate  acquaintance 
therewith,  that  few  dull  pages  will  be  encountered  in  the 
prosecution  of  the  proffered  course.  It  is  to  be  observed 
that  where  possible  a work  containing  a general  view  is 
included  as  the  framework  about  which  to  group  those  of 
less  general,  though  perhaps  of  more  interesting,  character. 

The  list  is  comprised  of  about  eighty  works,  the  total  cost  of 
which  would  not  exceed  $300.00.  Thus,  it  is  within  the  power 
of  any  group  of  battalion  or  regimental  officers  to  acquire  such 
a library  in  a short  time  without  overtaxing  the  indi\fidual, 
affording  to  the  whole  a course  of  reading  which  could  extend 
over  a period  of  from  five  to  ten  years  with  advantage,  the  more 
zealous  students  devoting  their  attention  to  technical  treatises 
on  strategy  and  tactics  along  with  the  works  enumerated. 


STUDY  AND  THE  VALUE  OF  THEORY 


XXV 


BIBLIOGRAPHY 

Macedonian  Wars..- 

1.  — Life  of  Alexander:  B.  I.  Wheeler. 

2.  — Alexander  the  Great:  Henderson. 
_3. — Alexander:  Dodge. 

Punic  Wars 

r 1.— Hannibal:  Dodge. 

L2. — Hannibal:  McDougall. 

Julius  Caesar ■j 

1.  — Caesar:  Dodge. 

2.  — Caesar’s  Gallic  Campaigns:  Holmes. 

Thirty  Years’  War,_ 
and  after | 

1.  — Gustavus  Adolphus  and  the  Development  of  the  Art 

of  War:  Dodge. 

2.  — Life  of  John  Churchill,  Duke  of  Marlborough: 

Wolseley. 

3.  — ^Prince  Eugene  of  Savoy:  Malleson. 

4.  — Turenne’s  Campaigns. 

Parliamentary  War....l. — Cromwell  as  a Soldier:  Baldock. 


Seven  Years’  War. .- 

1.  — History  of  Prussia  under  Frederick  the  Great:  Tuttle. 

2.  — Frederick  the  Great  and  the  Seven  Years’  War:  Long- 

mans. 

3. — Frederick  the  Great:  Dodge. 


American  Revolu- 
tion and  War  of-< 
1812 

1.  — American  Campaigns:  Steele. 

2.  — American  Revolution:  Fiske. 

3.  — Studies  Military  and  Diplomatic:  Adams. 

4.  — The  Revolutionary  War:  Greene. 

Napoleonic  Wars.. .- 

1.  — Jomini’s  Napoleon’s  Campaigns:  Halleck. 

2.  — Rise  of  Wellington:  Roberts. 

3.  — Life  of  Nelson:  Mahan. 

4.  — The  Peninsula  War:  Napier. 

5. — Napoleon  as  a General:  Von  Wartenburg. 

6.  — -The  Life  of  Wellington:  Hamley. 

7.  — The  Life  of  Wellington:  Maxwell. 

8.  — Waterloo — 1815:  Houssaye. 

9.  — Napoleon:  Dodge. 

10. — The  Decline  and  Fall  of  Napoleon:  Wolseley 

T j.  { 1. — Forty-one  Years  in  India:  Roberts, 

n lan  u my — Recollections  of  a Military  Life:  Adye. 


XXVI 


INTRODUCTION 


Crimean  War. . 
1854-5. 


1.  — The  War  in  the  Crimea:  Hamley. 

3. — Recollections  of  a Mihtary  Life:  Adye. 

2.  — The  Crimean  Diary:  Windham. 

(Consult  Kinglake’s  “Invasion  of  the  Crimea.”) 


1.  — American  Campaigns:  Steel. 

2.  — Stonewall  Jackson  and  American  Civil  War:  Render 

son. 

3.  — The  Crisis  of  the  Confederacy:  Battine. 

4.  — Military  Memoirs  of  a Confederate:  Alexander. 
American  Civil  War. ^ 5. — Battle  of  ChanceUorsville:  Hamlin. 

1861-5.  6. — Battle  of  the  Wilderness:  Schaaf. 

7.  — Studies  Military  and  Diplomatic:  Adams. 

8.  — Battles  and  Leaders  of  the  Civil  War. 

9.  — Science  of  War  (Portions  pertaining  to  Civil  War): 

Henderson. 

(Consult  “ Rebellion  Records.”) 


Seven  Weeks’  War 
( Austro-Prussian) . 
1866. 


1.  — The  Seven  Weeks’  War:  Hozier. 

2.  — Campaign  of  Koniggratz:  Wagner. 


1.  — With  Royal  Headquarters,  1870-71:  Verdy 

Vernois. 

2.  — My  Experiences  of  the  War  between  France 

Franco-German  War  J Germany:  Forbes. 

1870-1.  3. — The  Battle  of  Spicheren:  Henderson. 

4. — Franco-German  War:  Moltke. 

(Consult  German  Official  Account.) 


du 

and 


Russo-Turkish  War.^ 
1877-8. 


1.  — Russo-Turkish  War:  Hozier. 

2.  — Russian  Army  and  its  Campaigns  in  Turke5q  1877-8: 

Greene. 

3.  — Operations  of  Gen.  Gurko’s  Advance  Guard,  1877: 

Epauchin. 

4.  — Tactical  Studies  on  the  Battles  around  Plevna:  ^’on 

Trotha. 

5.  — Experiences  of  a Prussian  Officer  during  Russo- 

Turkish  War:  Von  Pfeil. 


Egyptian  Wars. 
1881-1898. 


1.  — General  Gordon:  Butler. 

2.  — With  Kitchener  to  lOiartoum:  Steevens. 

3.  — With  Fire  and  Sword  in  the  Sudan:  Slatin  Pasha. 

4.  — Recollections  of  a Military  Life:  Adye. 


STUDY  AND  THE  VALUE  OF  THEORY 


xxvu 


China-Japan  War. . / 1. — Japan-China  War:  Inouye. 

1894.  1 2. — China- Japan  War:  Vladimir. 

I Graeco-Turkish  War:  by  a German  Staff  Officer. 


Spanish  -American 
War.  1898.. 


1.  — Report  of  Santiago  Campaign:  Wagner. 

2.  — Santiago  Campaign:  Wheeler. 

.3. — The  War  with  Spain:  Lodge. 


South  African  War. 
1899-1901. 


1.  — Operations  ia  South  Africa:  U.  S.  War  Dept.  Reports. 

2.  — My  Experiences  of  the  Boer  War:  Count  Sternberg. 

3.  — The  War  in  South  Africa:  Mahan. 

4.  — The  Second  Boer  War,  1899-1900:  Wisser. 

5.  — German  Official  Account,  Paardeburg  to  Pretoria: 

DuCane.  (Trans.) 

Q. — Three  Years’  War:  De  Wet. 


Philippine  War  and 
Chinese  ReUef  Ex-^ 
pedition.  1898- 
1900 


1.  — Memories  of  Two  Wars:  Fimston. 

2.  — America  in  Chinese  Relief  Expedition:  Daggett. 

3.  — Operations  in  China:  U.  S.  W'ar  Dept.  Reports. 


1.  — A Staff  Officer’s  Scrap  Book:  Hamilton. 

2.  — From  the  Yalu  to  Port  Arthur:  Wood. 

Russo- Japanese  War. ^ 3. — The  Truth  about  the  War:  Tabumo. 

1903-5.  4. — History  of  War  in  Manchuria:  London  Times. 

5. — II.  S.  War.  Dept.  Reports. 

.6. — With  Kuroki  in  Manchuria:  Steevens. 


CLASSIFICATION  OF  FIELD  ARTILLERY 


There  seems  to  be  more  or  less  confusion  with  respect  to 
the  classification  of  Field  Artillery.  The  following  will, 
therefore,  prove  instructive. 

Most  of  the  difficulty  seems  to  come  from  a confusion  of 
the  terms  “siege  artillery”  and  “heavy  field  artillery,”  which 
are  taken  to  be  synonymous,  while  in  reality  they  are  not. 
A large  part  of  this  confusion  arises  from  a failure  to  know 
or  to  recognize  the  fact  that  heavy  field  artillery  is  a product 
of  almost  the  last  decade  only,  while  siege  artillery  is  a very 
old  designation  and  has  now  largely  lost  its  significance. 

In  separating  the  field  artillery  from  the  coast  artillery 
in  1907,  Congress  decreed  that  “the  field  artillery  is  the  artil- 
lery which  accompanies  an  army  in  the  field,  and  includes 
light  artillery,  horse  artillery,  siege  artillery,  and  mountain 
artillery,”  thus  uniting  under  one  caption  all  the  varieties 
of  mobile  artillery  at  that  time  in  our  service.  This  defini- 
tion, therefore,  also  indicates  the  scope  of  the  duties  of  the 
field  artillery. 

It  should  be  noted  that  the  significance  of  the  word  “field” 
is  here  considerably  extended,  and  is  made  general  instead 
of  referring  to  a special  class  of  artillery.  When  “field  artil- 
lery” is  spoken  of  abroad,  that  artillery  armed  with  the  3-in. 
or  75-mm.  gun  is  meant;  in  other  words,  it  is  a specific  class, 
whereas  with  us  the  term  is  a general  one,  including  a number 
of  varieties. 

Mountain  Artillery. — The  name  indicates  the  use.  This 
artillery,  primarily  intended  for  rough  country  impracticable 
for  wheels,  is  packed  on  animals.  The  gun  is  light,  weighing 
about  one-third  as  much  as  the  standard  light-battery  gun. 


XXIX 


XXX 


INTRODUCTION 


but  firing  a projectile  of  about  the  same  size.  From  these 
two  conditions  it  necessarily  follows  that  the  range  is  short, 
not  over  one-half  that  of  the  light-artillery  gun.  TMiile,  as 
stated,  normally  the  battery  is  transported  by  pack  trans- 
portation, in  many  countries  shafts  are  also  provided  in 
order  that  the  animals  may  be  relieved  when  practicable 
by  utilizing  draft.  This  is,  of  course,  easier  on  the  animals, 
but  many  officers  in  our  service  do  not  believe  in  ha\ung 
any  draft  for  two  reasons : First,  when  using  packs  the  shafts, 
which  must  also  be  packed,  catch  on  trees,  vines,  etc.,  and 
interfere  with  movements;  and,  second,  if  it  is  feasible  to 
use  draft  or  wheeled  transportation,  light  artillery  should  be 
substituted  for  mountain.  Our  mountain  artillery  is  at 
present  equipped  with  the  2.95-in.  Maxim-Nordenfeldt  gun, 
but  this  weapon  will  be  replaced  by  a 3-in.  mountain  howitzer 
firing  a 15-lb.  projectile.  In  this  class  of  artillery  the  weight 
should  not  exceed  about  300  lbs.  for  each  pack  animal. 

Light  Artillery. — This  designation,  which  is  one  of  long 
standing  in  our  service,  corresponds  to  the  special  designa- 
tion, “field  artillery,”  in  use  abroad.  In  all  countries  this 
artillery  is  very  similar,  the  projectile  weighing  about  15  lbs., 
and  the  range  being  about  7,000  yards.  But  in  speaking 
of  the  range,  it  must  be  borne  in  mind  what  is  most  needed 
in  war  is  not  extreme  range,  but  the  most  effective  range, 
and  that  the  effect  of  shrapnel  falls  off  quite  perceptibly 
beyond  3,000  yards.  Beyond  this  range  the  guns  shoot 
almost  as  accurately  as  below  it,  but  many  things  combine 
to  make  long-range  firing  more  or  less  ineffective.  With  the 
field  gun,  as  the  range  increases  more  and  more  ammunition 
is  necessary  to  produce  the  desired  effect.  This  is  due  to 
the  great  angle  of  fall  and  also  to  the  small  remaining  velocity 
making  the  shrapnel  more  and  more  local  in  its  effect,  while 
at  the  same  time  the  difficulty  of  observing  and  adjusting 
the  fire  increases  with  the  range,  and  accurate  observa- 
tion is  essential  to  prevent  waste  of  ammunition.  In  our 


CLASSIFICATION  OF  FIELD  ARTILLERY 


XXXI 


service,  light  artillery  is  armed  with  the  3-in.  rapid-fire  gun, 
throwing  a 15-lb.  projectile  and  having  a weight  of  about 
4,200  lbs.  behind  teams  of  six  horses. 

Horse  Artillery. — Horse  artillery  is  primarily  designed  to 
accompany  cavalry.  All  the  personnel  are  mounted  on 
horses.  It  is  readily  seen  that,  if^the  guns  are  to  keep  up  with 
the  cavalry,  every  effort  must  be  made  to  lighten  the  weight 
behind  the  teams,  and  hence  the  cannoneers,  instead  of  riding 
on  the  carriages,  are  provided  with  saddle-horses.  In  time 
of  peace  the  casual  observer  sees  little  difference  between 
light  and  horse  artillery,  but  every  war  brings  out  the  dis- 
tinction clearly.  When  the  ammunition  chests  are  full,  the 
forage  scant,  the  roads  bad,  and  the  work  continuous,  the 
difference  in  mobility  between  these  two  classes  of  artillery 
is  at  once  apparent.  Horse  artillery  is,  therefore,  designed 
not  only  to  accompany  the  cavalry,  but  also  to  reinforce 
parts  of  the  battlefield  as  quickly  as  possible.  The  Franco- 
German  war  shows  many  cases  where  the  horse  artillery, 
due  to  its  greater  mobility,  arrived  at  critical  times  several 
hours  ahead  of  the  light  or  field  artillery,  and  in  the  recent 
war  in  the  far  East  the  lack  of  horse  artillery  on  the  Japanese 
side  prevented  them  from  ever  converting  a Russian  retreat 
into  a rout.  In  some  countries  the  horse  artillery  is  provided 
with  a lighter  gun  and  carriage  than  has  the  light  artillery, 
and  the  gun  fires  a projectile  weighing  slightly  less.  In  our 
service  the  horse  artillery  has  the  same  gun  as  has  the  light 
artillery,  thus  avoiding  the  complication  in  ammunition 
supply  which  would  be  caused  by  the  introduction  of  another 
caliber.  Whether,  however,  the  gun  is  sufficiently  mobile 
is  a question  that  has  not  yet  been  determined.  The  English 
have  the  latest-adopted  horse-artillery  gun,  which  fires  a 12h- 
Ib.  projectile.  They  seem  to  be  very  much  pleased  with  their 
horse-artillery  gun.  One  solution  that  has  been  suggested  in 
our  service  is  to  use  the  present  gun  and  carriage  but  to  carry 
less  ammunition,  thus  reducing  the  weight  behind  the  teams. 


XXXll 


INTRODUCTION 


The  experience  of  all  wars  has  shown  that  the  work  of  horse 
artillery  is  arduous,  and  that  upon  returning  from  any  expedition 
the  horses  are  badly  in  need  of  rest.  In  our  service  it  is, 
therefore,  wisely  provided  that  the  harness  and  the  saddle 
horses  shall  be  interchangeable,  thus  providing  some  relief 
for  the  draft  horses.  Those  authorities  who  advocate  a special 
gun  for  the  horse  artillery  limit  the  weight  to  about  3,400  lbs. 
behind  a six-horse  team. 

Heavy  Field  Artillery. — This  is  the  most  recent  develop- 
ment of  field  artillery,  and  consequently  the  character  of 
the  material  and  the  use  to  which  it  will  be  put  are  not  as 
clearly  worked  out  as  with  other  classes  of  artillery.  The 
tendency  of  troops,  both  on  the  offensive  and  defensive,  to 
take  cover  has  steadily  increased  with  the  improvement  in 
guns  and  small  arms,  with  the  result  that  in  the  contest 
between  light  guns  and  cover  the  latter  reached  a point  where 
the  former  was  overmatched.  Theoretically,  the  advantage 
should  always  be  on  the  side  of  cover,  for  there  is  no  hmit 
to  the  amount  of  digging  that  could  be  done,  while  there  is 
clearly  a limit  to  the  weight  of  gun;  but,  practically,  the  ques- 
tion of  time  to  construct  the  cover  enters,  as  well  as  the  fact 
that  if  the  position  is  too  strong  to  be  attacked  troops  will  be 
maneuvered  out  of  it.  However,  it  is  recognized  that  the 
works  thrown  up  in  a day  or  two  are  beyond  the  power  of 
the  light  field  gun,  and  hence  the  heavy  field  gun  becomes 
necessary.  Such  artillery  is  a part  of  every  army,  and  foreign 
regulations  state  that  its  presence  may  be  expected  on  every 
battlefield  in  the  future.  The  gun  is  as  hea\'y  as  is  consistent 
with  giving  it  the  mobility  of  infantry  in  masses.  The  con- 
fusion in  our  service,  due  to  the  loose  use  of  the  term  "siege 
artillery,”  is  caused  by  failure  to  recognize  that  the  hea\>y 
field  artillery  accompanies  the  army  at  all  times  and  is  used 
on  practically  every  battlefield.  It  takes  up  the  work  where 
the  light  gun  leaves  off.  The  heavy  field  gun  in  our  service 


TABLE  OF  FIELD  CUN8,  1910. 


1 


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CLASSIFICATION  OF  FIELD  ARTILLERY  xxxiii 

is  the  4.7-in.  gun,  throwing  a 60-lb.  projectile,  the  carriage 
using  the  same  sights  as  those  of  the  other  guns  in  the  field 
artillery,  using  the  same  methods  of  checking  recoil  and  the 
same  system  of  fire  control,  and  requiring  no  special  anchor- 
age or  platforms,  and  thus  being  truly  field  artillery. 

Light  Howitzers. — The  flat  trajectory  fire  of  guns  must  be 
supplemented  by  curved  fire  in  order  to  reach  defenders 
behind  protection  or  for  the  purpose  of  destroying  the  pro- 
tection; hence,  both  the  light  and  the  heavy  field  guns  must 
be  supplemented  by  a howitzer.  The  3.8-in.  howitzer  now 
being  manufactured  by  the  Ordnance  Department  could  be 
truly  classified  as  a light  howitzer.  It  has  the  same  weight 
behind  the  six-horse  team  as  has  the  3-in.  gun,  and  throws 
a 30-lb.  projectile. 

The  Ordnance  Department  has  also  designed  a 4.7-in. 
howitzer,  throwing  a 60-lb.  projectile,  which  might  be  clas- 
sified as  either  a light  howitzer  or  a heavy  howitzer,  depending 
largely  upon  its  use,  this  use,  in  turn,  depending  largely  upon 
its  mobility.  The  howitzer  has  6,000  lbs.  behind  the  teams, 
and  if  these  are  composed  of  eight  horses  the  howitzer  could 
be  used  as  a light  howitzer,  while  if,  on  the  other  hand,  the 
teams  are  composed  of  but  six  horses,  it  would  fall  into  the 
class  of  heavy  howitzer. 

Heavy  Howitzers. — This  howitzer  is  designed  to  supple- 
ment the  4.7-in.  gun.  The  howitzer  designed  by  the  Ordnance 
Department  has  a 6-in.  cafiber  and  fires  a 120-lb.  projectile. 
The  weight  behind  the  teams,  8,000  lbs.,  is  the  same  as  with 
the  4.7-in.  field  gun.  This  howitzer,  like  both  of  the  others 
mentioned,  has  all  the  laying  and  sighting  appliances  of  the 
other  ordnance  of  the  field  artillery,  and  also  uses  the  same 
fire-control  system,  the  same  method  of  checking  recoil, 
requires  no  anchorage,  hold-fasts,  platforms,  or  any  prepara- 
tion previous  to  its  going  into  action.  It  is,  therefore,  clearly 
a field-artillery  weapon. 

All  the  ordnance  so  far  considered  fire  both  high-explosive 


XXXIV 


INTRODUCTION 


shell  and  shrapnel.  The  demolition  effects  of  the  high-explo- 
sive shell  are  sufficient  to  break  up  any  field  work  that  can 
be  constructed  by  the  labor  of  troops. 

Siege  Artillery. — The  term  “siege  artillery,”  correctly  used, 
refers  to  artillery  used  in  investing  a besieged  or  beleagured 
place.  Such  artillery  would  include  many  different  calibers. 
But  the  term  was  used  in  the  act  of  separating  the  coast  and 
the  field  artillery  on  account  of  our  having  in  service  at  that 
time  5-in.  siege  guns  and  7-in.  siege  howitzers.  These  pieces 
had  long  been  known  as  “siege  artillery,”  and  dated  back 
to  a time  prior  to  the  development  of  heavy  field  artillery, 
and,  consequently,  as  it  was  intended  that  the  field  artillery 
should  include  all  mobile  artillery,  the  designation  “siege” 
was  put  into  the  law.  Since  that  time,  however,  these  obsolete 
pieces  have  been  withdrawn  from  service  and  are  now  being 
replaced  by  a slightly  smaller  caliber  having  much  greater 
power  and  a weight  of  about  8,000  lbs.  to  be  drawn  by  eight 
horses  and  thus  being  mobile  enough  to  accompany  infantry 
in  masses. 

This  term  has  almost  lost  any  definite  meaning,  due  to  the 
fact  that  in  sieges  the  largest  gun  that  is  practicable  is  brought 
up  to  the  front  for  an  investment,  and  that  with  increased 
transportation  facilities  it  has  become  possible  to  bring  up 
heavier  and  heavier  guns.  Thus,  at  Port  Arthur  11-in.  mor- 
tars were  brought  up.  Such  weapons  do  not  form  part  of 
the  field  artillery,  though  it  may  be  necessary  to  have  this 
class  of  troops  handle  siege  guns.  There  is  no  distinct  line 
of  demarcation  between  heavy  field  artillery  and  siege  artil- 
lery. The  term  really  relates  more  to  the  use  to  which  the 
gun  is  put  than  to  its  caliber.  But  it  is  generally  understood 
that  such  artillery  comprises  guns,  howitzers,  mortars,  etc., 
that  are  not  permanently  horsed,  and  which  do  not  nonnally 
accompany  an  army,  but  which  are  brought  up  when  needed 
for  some  specific  purpose  by  utilizing  traction  engines,  rail- 
roads, or  any  similar  means  of  moving  the  guns,  and  that 


CLASSIFICATION  OF  FIELD  ARTILLERY 


XXXV 


platforms,  not  infrequently  made  of  concrete,  are  built,  and 
that  when  the  guns  are  placed  in  position  they  generally  stay 
there  until  the  siege  is  over.  In  European  armies  this  class  of 
ordnance  is  served  by  fortress  artillerymen,  a class  we  do  not 
have  in  the  United  States.  Most  European  nations  having 
a land  frontier  have  constructed  defensive  works  along  the 
frontier,  which  works  are  manned  by  guns  heavier  than  field 
guns  and  lighter  than  our  large  coast-artillery  guns,  and  these 
are  served  by  fortress  artillerymen.  When  these  men  are  no 
longer  needed  in  the  fortress  they  move  out  and  take  with 
them  such  of  the  ordnance  as  can  be  transported  by  the 
methods  previously  stated.  In  other  words,  these  fortress 
troops  are  an  intermediate  class  between  our  field  artillery 
and  our  coast  artillery.  No  provision  has  ever  been  made 
in  our  service  for  this  class  of  artillery,  and  probably  none 
ever  will  be,  and  therefore  the  question  as  to  whether  the 
field  or  the  coast  artillery  will  handle  such  guns  is  one  that 
has  never  been  settled.  There  can,  however,  be  no  doubt 
but  that  heavy  field  artillery,  including  all  the  calibers  that 
have  been  mentioned  in  this  article,  properly  belongs  to  field- 
artillery  troops,  and,  under  the  law,  must  be  handled  by  them. 


PART  I 

AN  ELEMENTARY  COURSE  OF 
MATHEMATICS  FOR  FIELD 
ARTILLERYMEN 


Taken  from  Artillery  Circular  H,  June  1,  1893. 


I 


i 


COURSE  IN  MATHEMATICS  FOR 
ARTILLERY  GUNNERS 


CHAPTER  I 

DEFINITIONS  AND  USE  OF  MATHEMATICAL  SIGNS 

Mathematics  is  the  science  of  quantity. 

Science  is  an  arrangement  of  the  principles  of  any  subject 
in  regular  and  proper  order. 

Quantity  is  anything  that  can  be  increased,  diminished,  or 
measured.  To  measure  a quantity  is  to  find  how  many  times 
it  contains  some  other  quantity  of  the  same  kind,  called  the 
unit  of  measure.  A unit  is  a single  thing  of  any  kind. 

In  pure  mathematics,  or  mathematics  which  considers 
quantity  without  regard  to  matter,  there  are  but  eight  kinds 
of  quantity,  and  hence  only  eight  kinds  of  units,  viz. : Units  of 
number,  of  length,  of  surface,  of  volume,  of  weight,  of  time,  of 
currency,  and  of  angular  measure. 

Quantity  includes  number  and  magnitude.  A number  is 
one  or  more  units;  a magnitude  anything  that  can  be  measured. 
Number  answers  the  question  How  many?  magnitude.  How 
much? 

Arithmetic  is  the  science  of  numbers.  In  arithmetic  num- 
bers are  usually  expressed  by  figures;  as  1,  2,  3,  etc.  Numbers 
are  called  abstract  when  the  kind  of  unit  is  not  named;  as  one, 
two,  three,  etc.;  denominate,  when  the  unit  is  named;  as  one 
yard,  two  pounds,  three  seconds,  etc. 

A problem  is  a question  regarding  quantity  proposed  for 
solution. 


3 


4 


GUNNERY 


A solution  is  a statement  of  the  mathematical  work  done 
to  obtain  the  answer  to  a problem. 

A rule  is  a general  direction  for  solving  problems  of  the 
same  kind. 

In  stating  mathematical  work  it  is  often  convenient  to 
indicate  by  characters,  called  mathematical  signs,  what  is  to 
be  done  with  the  quantities  considered,  or  the  relations  which 
exist  between  them. 

The  signs  most  used  in  arithmetic  are  +,  — , X,  and 
V , which  indicate  work  to  be  done,  and  are  called  signs  of 

operation,  and  , (),  [],  =,  :,  and  which  show  relation 

between  or  among  quantities,  and  are  called  signs  of  relation. 

+ is  the  sign  of  addition,  and  is  read  ^'plus.”  The  numbers 
between  which  it  is  placed  are  to  be  added.  Thus:  4 + 2,  is 
read  ‘‘4  plus  2,”  and  equals  6. 

— is  the  sign  of  subtraction,  and  is  read  “minus.”  When 
placed  between  two  numbers,  the  one  on  the  right  is  to  be 
taken  from  that  on  the  left.  Thus:  5 — 3 is  read  “5  minus  3,” 
and  equals  2. 

X is  the  sign  of  multiplication,  and  is  read  “multiplied  by,” 
or  “times.”  The  numbers  between  which  it  is  placed  are  to 
be  multiplied  together.  Thus  4 X 5 is  read  ‘^4  multiplied  by 
5,”  or  “4  times  5,”  and  equals  20. 

^ is  the  sign  of  division,  and  is  read  “divided  by.”  WTien 
placed  between  two  numbers,  the  one  on  the  left  is  to  be  divided 
by  that  on  the  right.  Thus:  6 4-  3 is  read  “6  divided  by  3,” 
and  equals  2. 

, 0,  and  []  are  signs  of  aggregation,  or  of  bringing 

together.  The  first  is  the  vinculum-,  the  second,  the  paren- 
theses-, the  third,  the  brackets.  They  are  used  for  the  same 
purpose — to  connect  several  quantities.  Numbers  placed 
under  the  vinculum,  or  within  the  parentheses  or  brackets,  are 
to  be  considered  as  one  quantity.  Thus:  6 — 3 + 2,  or  6 — 
(3+2),  or  6 — [3+2]  means  that  the  sum  of  3+2  is  to  be  taken 
from  6.  Brackets  are  ordinarily  used  only  when  the  total 


DEFINITIONS  AND  USE  OF  MATHEMATICAL  SIGNS 


5 


relation  can  not  be  shown  by  means  of  a single  vinculum  or 
parentheses. 

= is  the  sign  of  equality,  and  is  read  “is  equal  to,”  or 
“equals”  Quantities  between  which  it  is  placed  are  equal. 
Thus:  3+2X4  = (6+4)X2  = [(3+2)x(9-l)]-f-2  = 20. 

V is  the  radical  sign]  :,  the  sign  of  ratio]  the  sign  of 
proportion.  Their  uses  will  be  explained  hereafter. 

Arithmetic  depends  on  the  general  principle  that  any 
number  may  be  increased  or  diminished.  The  fundamental 
operations  of  arithmetic  are  addition,  subtraction,  multiplica- 
tion, and  division.  Multiplication  is  simply  a short  method 
of  adding  equal  numbers;  division,  a short  method  of  making 
several  subtractions  of  the  same  number.  Thus:  5 can  be 
multiplied  by  4 by  adding  four  5’s  together;  and  20  can  be 
divided  by  5,  or  how  many  times  20  contains  5 can  be  found  by 
subtracting  four  5’s  from  20. 

Numbers  are  therefore  classified  as  positive  numbers,  or 
numbers  to  be  added  together;  and  negative  numbers,  or  num- 
bers to  be  subtracted  from  positive  numbers,  but  added  to 
other  negative  numbers.  Positive  numbers  are  preceded  by 
the  sign  negative  numbers  by  the  sign  — . When  a num- 
ber has  no  sign  before  it,  it  is  considered  positive. 

In  every  mathematical  expression  a-f-  or  a—  affects  the 
whole  result  of  the  work  indicated  between  it  and  the  next  follow- 
ing -f-  or  — , or,  between  it  and  the  end  of  the  expression.  In 
no  case  can  a X or  a -t-  affect  any  quantity  before  the  preceding, 
or  beyond  the  following  -1-  or  — . Thus:  in  the  expression 
54-7X3X6—4X3,  the  -f-  indicates  the  addition  of  126,  not 
of  7 only;  and  the  — indicates  the  subtraction  of  12.  The 
same  meaning  is  better  expressed  by  5-t- (7X3X6) — (4X3). 

The  signs  X and  simply  show  what  operations  are  to 
be  performed  on  the  positive  or  negative  numbers  which  pre- 
cede them.  When  they  occur  in  succession  they  have  their 
effects  in  the  order  of  their  occurrence.  Thus:  in  the  expres- 
sion [30  — (6X4)] 3,  the  sign  X shows  that  6 is  to  be  multi- 


6 


GUNNERY 


plied  by  4,  but  it  does  not  show  what  is  to  be  done  with  the 
resulting  24;  this  is  shown  by  the  — . 24  is  to  be  taken  from 
30,  and  the  remainder  divided  by  3. 

PROBLEMS. 

1.  4X3+7x2-9X3+6X4-3X3  = what?  Ans.  14. 

Solution:  4X3  = 12;  7X2  = 14;  -9X3= -27;  6X4  = 24; 

— 3X3=— 9.  Grouping  according  to  the  + and  — signs, 
and  adding,  we  have,  12+14+24  = 50;  and  —27  — 9=— 36. 
Therefore,  50  — 36  = 14,  Ans. 

2.  8X2  — 94-3+4X5  — 6-^3  — 7X5  = what?  Ans.  —4. 

Solution:  16  — 3+20  — 2 — 35.  Grouping  and  adding,  we 
have,  36  — 40=— 4,  Ans. 

3.  214-3X7-1 XI 4- lX44-2+184-3X6-^(2X2)  + (4-2+6 

— 7)  X4X64-8  = what?  Ans.  59. 

Solution:  Performing  operations  indicated  between  + and 

— signs,  we  have  49  — 2+9+3,  or  61—2  = 59,  Ans. 

4.  16X44-8-7+484-16-3+24X64-48-4X94-12-1  = 

what?  Ans.  0. 

5.  (164-16X964-8-7-5+3)X  [(244-4)4-3-l]  + (9l4-13X7 

— 45  — 3)X9  = what?  Ans.  12. 

6.  (12+4X9T3)X  [(2+5X24-1+4X3-10)4-2-1]4-[28- 

2X  (3X2+84-4) —2]  = what?  Ans.  12. 


CHAPTER  II 


COMMON  FRACTIONS 

A fraction  is  one  or  more  equal  parts  of  a divided  unit. 

A whole  number  is  one  or  more  units. 

A mixed  number  consists  of  a whole  number  and  a fraction. 

Fractions  are  divided  into  two  classes — common  fractions 
and  decimal  fractions;  the  former  are  ordinarily  called  simply 
fractions;  the  latter,  when  expressed  as  hereafter  explained, 
decimals. 

A common  fraction  is  expressed  by  writing  one  number 
above  and  another  below  a line.  Thus:  | is  a common  frac- 
tion which  is  read  “three-fourths.”  The  number  above  the 
line  is  called  the  numerator;  that  below,  the  denominator. 
The  numerator  and  denominator  are  called  the  terms  of  the 
fraction. 

A proper  fraction  is  one  whose  numerator  is  less  than  its 
denominator;  as,  |,  f, 

An  improper  fraction  is  one  whose  numerator  is  equal  to 
or  greater  than  its  denominator;  as  f,  f?  I- 

A whole  number  may  be  expressed  as  an  improper  fraction 
by  writing  1 for  its  denominator.  Thus  4 = ^;  5 = f. 

A mixed  munber  may  be  expressed  as  an  improper  fraction 
by  multiplying  the  whole  number  by  the  denominator  of 
the  fraction,  to  the  product  adding  the  numerator  and  writing 
the  sum  over  the  denominator.  Thus:  2f  = V;  3f  = V. 

Cancellation. 

Cancellation  is  a process  by  which  operations  in  fractions 
may  often  be  shortened.  It  depends  on  the  principle  that  if 

7 


8 


GUNNERY 


both  terms  of  an  expression,  written  as  a fraction  and  in 
which  the  terms  are  products  of  two  or  more  numbers,  be 
divided  by  the  same  number  the  value  of  the  expression  vdll 
not  be  changed.  Any  number  that  will  exactly  divide  both 
terms  is  called  a common  factor. 

A factor  of  a number  is  any  number,  except  1 and  the  num- 
ber itself,  that  will  exactly  divide  it. 

Cancellation  consists  in  omitting  or  canceling  all  common 
factors  in  an  expression  such  as  that  just  referred  to.  To 
perform  this  operation — 

Cancel  all  common  factors,  and  divide  the  product  of  the 
remaining  factors  of  the  numerator  hy  the  product  of  the  remain- 
ing factors  of  the  denominator. 

Thus-  63X  12_/?^X^X3X3XfX^  _9 

42X  16~/X^X^X^X2X2X2  s' 

If  all  the  factors  of  either  the  numerator  or  denominator 
are  canceled,  1 must  be  written  for  the  last  factor  canceled. 

Reduction  of  Fractions. 

Reduction  of  fractions  consists  in  changing  their  form  with- 
out altering  their  value. 

Case  I. — To  reduce  a fraction  to  its  lowest  terms. 

A fraction  is  reduced  to  its  lowest  terms  when  all  factors 
common  to  both  terms  have  been  canceled. 

Rule. — Cancel  all  common  factors. 

PROBLEMS. 

Reduce  to  their  lowest  terms — 


1. 

Ans. 

1. 

2. 

144 

i1^* 

Ans. 

3. 

lAA 
2 10* 

Ans. 

4. 

m. 

Ans. 

13 

17* 

5. 

ill. 

Ans. 

H. 

6. 

m. 

Ans. 

li 

COMMON  FRACTIONS 


9 


Case  II. — To  reduce  fractions  to  a common  denomi- 
nator. 

Fractions  have  a common  denominator  when  their  denom- 
inators are  alike. 

Before  performing  the  operation,  express  mixed  numbers 
as  improper  fractions,  and  reduce  all  fractions  to  their  lowest 
terms. 

Rule. — Multiply  both  terms  of  each  fraction  hy  the  denomi- 
nators of  all  the  other  fractions. 


Rule. — Reduce  the  fractions  to  a common  denominator,  add 
their  numerators,  and  write  the  sum  over  the  common  denominator. 

When  there  are  mixed  numbers,  add  whole  numbers  and 
fractions  separately  and  then  add  their  sum.  After  adding, 
reduce  the  result  to  its  lowest  terms. 


Rule. — Reduce  the  fractions  to  a common  denominator  and 
write  the  difference  of  their  numerators  over  the  common  denom- 
inator. 


PROBLEMS. 

Reduce  to  a common  denominator 


Addition  of  Fractions. 


PROBLEMS. 


1.  3 +f — what?  Ans.  2Jf. 

2.  f +^+2^+11  = what?  Ans.  1-^. 

3.  i®o+A+A+2^  = what?  Ans.  3|i. 

4.  l^-l-2-|-t-3j*f-4|  = what?  Ans. 


Subtraction  of  Fractions. 


10 


GUNNERY 


When  there  are  mixed  numbers  and  the  numbers  are  small, 
express  them  as  improper  fractions  and  then  subtract;  if  the 
numbers  are  not  small,  subtract  whole  numbers  and  fractions 
separately  and  then  unite  the  results. 

If  the  fraction  of  the  subtrahend  is  greater  than  that  of 
the  minuend,  take  a unit  from  the  whole  number  of  the  minu- 
end, add  to  its  fraction,  and  then  subtract.  After  subtracting, 
reduce  the  remainder  to  its  lowest  terms. 

PROBLEMS. 

1.  ^2=what?  Ans.  H. 

2.  If— ^3=  what?  Ans.  If. 

3.  7^^  — 3|=what?  Ans.  3H. 

4.  5f|  — 2f  = what?  Ans.  3^2t» 

Multiplication  of  Fractions. 

Rule. — Multiply  the  numerators  together  for  a new  numerator 
and  the  denominators  for  a new  denominator. 

Before  multiplying,  indicate  the  operation  and  employ 
cancellation  when  applicable.  Whole  and  mixed  numbers 
should  be  expressed  as  improper  fractions. 


PROBLEMS. 


1. 

HXi\=what?  Ans. 

2. 

45  = what?  Ans.  35. 

3. 

32X2f  = what?  Ans.  76. 

4. 

121X31^  = what?  Ans.  40|. 

5. 

|XiXtTX3^X3i  = what?  Ans. 

4. 

6. 

3|X4|X5|X|Xt®jX6|  = what? 

Ans.  49. 

Division  of  Fractions. 

Rule. — Invert  the  terms  of  the  divisor  and  multiply  the  result- 
ing fraction  by  the  dividend. 


COMMON  FRACTIONS 


11 


Before  multiplying,  indicate  the  operation  and  employ 
cancellation  when  applicable.  Whole  and  mixed  numbers 
should  be  expressed  as  improper  fractions. 

PROBLEMS. 

1.  — what?  Ans.  1|. 

2.  If -i- 5 = what?  Ans. 

3.  19|-f-l|  = what?  Ans.  10|. 

4.  8g-j-f  = what?  Ans.  12|. 

5.  73|-^9|  = what?  Ans.  7|. 

6.  54|-|-^25|  = what?  Ans.  2|. 

GENERAL  PROBLEMS. 

1.  3i+4|-5i+16|-7H+10-14f  = what?  Ans.  6f|. 

2.  TVX2|XfVXl9|  = what?  Ans.  7jj. 

3.  (|XfX14^)^(AXfX13|)=what?  Ans.  6yV 

4.  [(4iX4|X4|)-l]-n[(4|x4|)-l]=what?  Ans.  4ff. 

5.  [(2+i)-(3+i)]-[(2-i)X(4-3f)]  = what?  Ans.  m. 

6.  ^X14^X^X^X^X6  = what?  Ans.  13^. 


CHAPTER  III 


DECIMAL  FRACTIONS 

A decimal  fraction  is  a fraction  whose  denominator  is  10, 
or  some  product  of  10  expressed  by  1 with  ciphers  annexed. 
Thus:  tV,  foVo  are  decimal  fractions. 

Decimal  fractions  are  ordinarily  expressed  by  writing  the 
numerator,  with  ciphers  prefixed  when  necessary,  after  a dot, 
or  period  (.),  called  the  decimal  point,  and  omitting  the  denom- 
inator. Decimal  fractions  when  so  written  are  called  decimals. 

The  places  of  figures  on  the  right  of  the  decimal  point  are 
called  decimal  places;  the  first  is  tenths;  the  second,  hundredths; 
the  third,  thousandths;  the  fourth,  ten-thousandths;  and  so  on. 
Thus:  At  is  written  .1,  and  read  “one-tenth”;  xw  is  written 
.04,  read  ‘ ‘four  hundredths  ’ ’;  iffo  is  written  .031,  read  ‘ ‘ thirty- 
one  thousandths”;  is  written  .0517,  read  “five  hundred 

and  seventeen  ten-thousandths.”  From  this  it  is  seen  that  the 
denominator  of  the  decimal  fraction  corresponding  to  any 
decimal  is  1 with  as  many  ciphers  annexed  as  there  are  deci- 
mal places  in  the  decimal;  and  that  any  decimal  is  read  by 
reading  the  number  after  the  decimal  point  as  a numerator, 
and  adding  to  the  number  thus  read  the  name  of  the  last,  or 
right-hand,  decimal  place. 

A pure  decimal  consists  of  single  figures  or  ciphers  in  its 
decimal  places  only;  as  .215. 

A mixed  decimal  consists  of  a whole  number  and  a pure 
decimal;  as  3.215. 

A complex  decimal  consists  of  a pme  or  mixed  decimal  and  a 
common  fraction;  as  3.215y. 


12 


DECIMAL  FRACTIONS 


13 


Reduction  of  Decimals. 

Reduction  of  decimals  consists  in  changing  their  form  with- 
out altering  their  value. 

Case  I. — To  reduce  a decimal  to  a common  fraction. 
Rule. — Write  the  decimal  as  a decimal  fraction  and  reduce 
this  fraction  to  its  lowest  terms. 

PROBLEMS. 

Reduce  .25  to  a common  fraction. 

Solution:  .25  = ro\  = j,  Ans. 

PROBLEMS. 

Reduce  to  common  fractions — 

1.  .25625.  Ans. 

2.  .003125.  Ans. 

3.  2.125.  Ans.  2|. 

4.  19.01750.  Ans.  19j^. 

5.  3.33i  Ans.  3i 

6.  11. Of.  Ans.  lliV. 

Case  II. — To  reduce  common  fractions  to  decimals. 
Rule. — Annex  ciphers  to  the  numerator  and  divide  it  hy 
the  denominator.  Then  point  off  from  the  right  of  the  quotient 
as  many  decimal  places  as  there  are  ciphers  annexed. 

PROBLEM. 

Reduce  | to  a decimal. 

Solution: 

.125,  Ans. 

Any  fraction  in  its  lowest  terms  having  in  its  denominator 
any  factor  other  than  2 or  5 can  not  be  reduced  to  a pure 
decimal.  Thus:  yV=-0833f,  or  .0833+;  and  | = .1666f,  or 


14 


GUNNERY 


.1667  — . The  sign  + is  used  at  the  end  of  a decimal  to  indi- 
cate that  the  last  figure  is  too  small;  the  sign  — , to  indicate 
that  it  is  too  great. 

By  the  rule,  a mixed  number  may  be  converted  into  a 
mixed,  or  a complex,  decimal;  and  a complex  decimal  having 
no  other  factor  than  2 or  5 in  the  denominator  of  the  common 
fraction  into  a pure  decimal.  Thus:  9j  = 9.25,  since  | = .25; 
3|  = 3.33|,  since  ^ = .33|,  and  .26^V  = *2604,  since  ^^^  = .04. 

PROBLEMS. 

Reduce  to  decimals — 

1.  if.  Ans.  .46875. 

2.  /j.  Ans.  .078125. 

3.  Ans.  .05078125. 

4.  42A.  Ans.  42.1875. 

5.  19/o.  Ans.  19.0375. 

6.  2.0sk.  Ans.  2.0003125. 

Addition  of  Decimals. 

Rule. — Write  the  numbers  to  be  added  so  that  the  decimal 
points  shall  be  in  the  same  column;  then  add  as  in  whole  numbers 
and  place  the  decimal  point  in  the  sum  directly  under  the  decimal 
points  above. 

Complex  decimals,  if  there  be  any,  must  be  made  pure  as 
far  as  the  decimal  places  extend  in  the  other  numbers. 

PROBLEMS. 

1.  14.034-t-25-b.0000625-b .0034  = what?  Ans.  39.0374625. 

2.  216.8630H-48.1057  + .029+1.3  = what?  Ans.  266.29771. 

3.  16|-(-.37|+3.4|-[-.000|  = what?  Ans.  3.9802V- 

4.  .1 H+. 66661 -h. 2222221  = what?  Ans.  1. 

5.  35. -1-3.5 -b  .354- .035  = what?  Ans.  38.885. 

6.  .14f-|-..018f-|-920-b.0139f  = what?  Ans.  920.1754. 


DECIMAL  FRACTIONS 


15 


SUBTKACTION  OF  DECIMALS. 

Rule. — Write  the  less  number  under  the  greater  so  that  the 
decimal  'points  shall  he  in  the  same  column;  then  subtract  as  in 
'whole  numbers  and  place  the  decimal  point  in  the  remainder 
directly  under  those  above. 

If  either  or  both  of  the  decimals  be  complex,  extend  them 
to  the  same  decimal  place  before  subtracting. 

If  the  greater  number  has  not  as  many  decimal  places  as 
the  smaller,  annex  O’s  until  it  has  the  same. 

PROBLEMS. 

1.  19.54 -8.00717  = what?  Ans.  11.53283. 

2.  19.  — 8.999i  = what?  Ans.  lO.OOOf. 

3.  3.701-2.41  = what?  Ans.  1.251. 

4.  1.169f-.93#^  = what?  Ans.  .238f. 

5.  4.9|  — .01^  = what?  Ans.  4.9225. 

6.  .Or^ —.001  = what?  Ans.  0. 

Multiplication  of  Decimals. 

Rule. — Multiply  as  in  whole  numbers  and  point  off  in  the 
product,  from  the  right  hand,  as  many  decimal  places  as  there 
are  in  both  numbers  multiplied  together;  if  there  be  not  so  many  in 
the  product,  supply  the  deficiency  by  prefixing  O’s. 

PROBLEMS. 

1.  64.01  X. 32  = what?  Ans.  20.4832. 

2.  34.x. 193  = what?  Ans.  6.562. 

3.  2.7X.4i  = what?  Ans.  1.134. 

4.  21.0375X4.441  = what?  Ans.  93.5. 

5.  .02JX  600  = what?  Ans.  13.5. 

6.  1. 006 X. 0001=  what?  Ans.  .0001006. 


16 


GUNNERY 


Division  of  Decimals. 

Rule. — Divide  as  in  whole  numbers  and  point  off  in  the 
quotient,  from  the  right  hand,  as  many  decimal  places  as  those 
in  the  dividend  exceed  those  in  the  divisor;  if  there  be  not  so  many 
in  the  quotient,  supply  the  deficiency  by  prefixing  O’s. 

When  there  are  more  decimal  places  in  the  divisor  than  in 
the  dividend,  annex  O’s  to  the  latter  until  the  number  in  both 
is  the  same.  The  quotient  will  then  be  a whole  number. 

When  it  is  necessary  to  continue  the  division  farther  than 
the  figures  of  the  dividend  will  allow,  annex  O’s  and  consider 
them  as  decimal  places  of  the  dividend. 

PROBLEMS. 

1.  .0001-^.01  = what?  Ans.  .01. 

2.  1,000-^.001=  what?  Ans.  1,000,000. 

3.  .0001  = 1000  = what?  Ans.  .0000001. 

4.  12.9 -=8.256  = what?  Ans.  1.5625. 

5.  3. 15-^375  = what?  Ans.  .0084. 

6.  10.1  = 17  = what?  Ans.  .59412  — . 


CHAPTER  IV 


TABLES  OF  MEASURE 


In  pure  mathematics,  as  before  stated,  there  are  but  eight 
different  kinds  of  quantity.  For  measuring  each  kind  of 
quantity,  there  are,  however,  one  or  more  systems  of  measure- 
ment, and  each  system  has,  for  convenience,  a number  of  sub- 
divisions. Quantities  expressed  in  terms  of  the  same  sub- 
division are  said  to  be  of  the  same  denomination. 

A table  of  measure  is  a series  of  numbers  showing  the  rela- 
tion between  the  different  subdivisions  of  a system  of  measure- 
ment for  a particular  kind  of  quantity. 

A measure  is  a unit  for  measuring  quantities  of  the  same 
denomination. 

A standard  unit  is  a measure  made  a standard,  by  law  or 
custom,  for  comparison  of  all  measures  of  the  same  system. 

The  following  are  some  of  the  tables  of  measure  in  ordinary 
use. 


Long  Measure — English  System  (established  in  United 
States  by  act  of  Congress  in  1834). 


Measures  of  Length. 


TABLE. 


12  inches,  marked  in.,  make 


1 foot,  marked  ft. 


3 feet, 

5|  yards, 
320  rods. 


make  1 yard,  marked  yd. 
make  1 rod,  marked  rd. 
make  1 mile,  marked  mi. 


17 


18 


GUNNERY 


EQUAL  QUANTITIES. 

1 mi.  = 1,760  yds.  = 5,280  ft. 

For  measuring  horses,  the  hand  = 4L  in.  is  the  unit;  for 
depths  at  sea,  the  fathom  = Q ft.;  for  speed  of  vessels,  the  knot 
= 1|  mi. 

Long  Measure — Metric,  or  French,  System  (author- 
ized in  the  United  States  by  act  of  Congress  in  1866). 


TABLE. 


10  millimeters,  marked  mm.,  make  1 centimeter,  marked  cm. 
10  centimeters,  make  1 decimeter,  marked  dm. 

10  decimeters,  make  1 meter,  marked  m. 

10  meters,  make  1 dekameter,  marked  Dm. 

10  dekameters,  make  1 hektometer,  marked  Hm. 

10  hektometers,  make  1 kilometer,  marked  Km. 


The  millimeter  and  centimeter  are  generally  used  in  measur- 
ing very  short  lengths;  the  meter,  for  ordinary  lengths;  and  the 
kilometer,  for  long  distances. 


Denomination. 
1 millimeter. 

1 centimeter. 

1 meter. 

1 kilometer. 


COMPARATIVE  TABLE. 

Legal  Value. 
.03937  inch. 

.3937  inch. 

39.37  inches. 
.62137  mile. 


Approximate  Value, 
ih  in. 
f in. 

3 ft.  3f  in. 

I nai. 


Measures  of  Surface. 
Square  Measure — English  System. 


TABLE. 

144  square  inches  {sq.  in.)  make  1 square  foot,  marked  sq.  ft. 

9 sq.  ft.  make  1 square  yard,  marked  sq.  yd. 


TABLES  OF  MEASURE 


19 


These  measures  are  used  for  ordinary  surfaces  other  than 
land. 

Square  Measure — Metric  System. — The  square  meter, 
marked  and  its  subdivisions  are  used  for  measuring  ordi- 
nary surfaces  other  than  land. 

COMPARATIVE  TABLE. 

Denomination.  Legal  Value.  Approximate  Value. 

1 square  meter.  1.196  sq.  yds.  lOf  sq.  ft. 

Measures  of  Volume. 

Cubic  Measure — Engish  System. 

TABLE. 

1,728  cubic  inches  {cu.  in.)  make  1 cubic  foot,  marked  cu.  ft. 

27  cu.  ft.  make  1 cubic  yard,  marked  cu.  yd. 

For  mesLsming  firewood,  the  cord  = 4 ft.X4  ft.  X8  ft.  = 128 
cu.  ft.,  is  the  unit;  for  measuring  hoard,  the  board  foot  = 12  in. 
X 12  in.  X 1 in. 

Cubic  Measure — Metric  System. 

The  cubic  centimeter  (cm^)  and  cubic  meter  {m^)  are  used  for 
measuring  ordinary  volumes. 

COMPARATIVE  TABLE. 

Denomination.  Legal  Value.  Approximate  Value. 

1 cubic  centimeter.  .061  cu.  in.  ^ cu.  in. 

1 cubic  meter.  1.308  cu.  yds.  cu.  ft. 

In  the  English  system,  for  measures  of  length,  surface,  and 
volume,  a yard  measure  made  of  bronze  is  the  standard,  unit; 
in  the  metric  system,  a standard  meter,  made  of  platinum. 


20 


GUNNERY 


Measures  of  Capacity. 


Dry  Measure — English  System. — Used  for  measuring 
all  dry  articles. 


The  standard  unit  for  dry  measure  in  the  United  States  is 
the  “ Winchester  bushel,”  which  contains  2,150.42  cu.  in.  A box 
16  in.XlG  in.  X 16.8  in.  contains  2,150.4  cu.  in.,  or  1 bushel, 
very  nearly;  a box  8 in. X 8.4  in.X8  in.,  1 peck. 

Liquid  Measure — English  System. — Used  for  measur- 
ing liquids. 

TABLE. 

4 gills,  marked  gi.,  make  1 pint,  marked  pt. 

2 pts.  make  1 quart,  marked  qt. 

4 qts.  make  1 gallon,  marked  gal. 

The  standard  unit  for  liquid  measure  in  the  United  States 
is  the  gallon,  which  contains  231  cu.  in.  A box  6 in.X6  in. 
X6.4  in.  contains  230.4  cu.  in.,  or  1 gallon,  very  nearly;  a box 
4 in.X4  in.  X 3.6  in.,  1 quart. 

Dry  and  Liquid  Measures — Metric  System. 

The  liter,  marked  I,  and  the  hektoliter,  marked  HI,  are  the 
measures  ordinarily  used. 


TABLE. 


2 pints,  marked  pt.,  make  1 quart,  marked  qt. 


8 qts., 
4 pks. 


make  1 peck,  marked  pk. 
make  1 bushel,  marked  hu. 


COMPARATIVE  TABLE. 


Denomination. 
1 liter. 

1 hektoliter. 


Legal  Value.  Approximate  Value. 
1.0567  qts.  1 qt. 

2.8375  bu.  2 bu.  3^  pks. 


TABLES  OF  MEASURE 


21 


Measures  of  Weight. 

English  System. — Avoirdupois  weight,  used  for  weighing 
all  ordinary  articles. 


TABLE. 

16  drams,  marked  dr.,  make  1 ounce,  marked  oz. 

16  oz.  make  1 pound,  marked  lb. 

25  lbs.  make  1 quarter,  marked  qr. 

4 qrs.  make  1 hundredweight,  marked  cwt. 

20  cwt.  make  1 ton,  marked  T. 

In  England  1 cwt.  = 112  lbs;  1 ton  = 2,240  lbs.  These 
measures  are  used  in  the  United  States  for  coal  and  iron. 

In  the  United  States  artillery,  what  is  called  the  ‘‘troy 
grain”  (7,000  to  1 pound  avoirdupois)  is  taken  as  the  standard 
for  weight. 

Metric  System. — The  kilogram,  commonly  called  the 
“kilo,”  and  the  metric  ton  are  used  in  weighing  ordinary  arti- 
cles; the  gram,  in  cases  where  great  accuracy  is  required. 

comparative  table. 

Legal  Value.  Approximate  Value. 
2.2046  lbs.  av.  2-g-  lbs. 

2,204.6  lbs.  av.  1 T.  204f  lbs. 
15.432  grains  troy.  15J  grains. 

Measures  of  Angles. 

A plane  angle,  or  an  angle  as  it  is  usually  called,  is  the  quan- 
tity by  which  two  straight  lines,  starting  from  a point,  separate 
from  each  other;  or,  as  often  defined  for  simplicity,  it  is  the 
opening  between  two  lines  which  meet  at  a point.  The  point 
is  called  the  vertex]  the  lines,  the  sides  of  the  angle. 


Denomination. 
1 kilo. 

1 metric  ton. 

1 gram. 


22 


GUNNERY 


Thus  if  two  lines,  AB  and  AB^,  at  first  coincide,  and  one  of 
them  be  then  moved  in  the  plane  of  the  paper  to  the  positions 
AB^,  and  so  on,  until  they  again  coincide,  the 

opening  between  the  lines,  or  the  angle,  will  be  increased, 
successively,  from  its  least  to  its  greatest  value  for  one  revo- 
lution. 

Any  point  on  the  line  AB^,  as  will  describe  a curved  line 
called  a circumference  of  a circle.  The  portions 

B" 


/ \ \ 

/ ;b 

i \ 

\ \ 
\ 

/'  / 
/ / 
/ / 
/ 

✓ / 

LV  y/ 

B"' 

Fig.  1. 

hV'"  of  the  circumference  show  the  sizes  to  which  the  angle, 
at  first  equal  0,  has  been  successively  increased;  and  since 
these  portions  would  hear  the  same  relation  to  each  other,  no  matter 
what  point  on  the  line  AB^  were  chosen,  they  may  be  assumed 
as  the  measures  of  the  angles.  For  measuring  angles  circmn- 
ferences  are  ordinarily  divided  as  follows: 

TABLE. 

60  seconds,  marked  ",  make  1 minute,  marked  '. 

60'  make  1 degree,  marked  °. 

360°  make  1 circumference,  marked  c. 


CHAPTER  V 


DENOMINATE  NUMBERS 

A denominate  number  is  one  in  which  a quantity  is  given  in 
one  denomination;  as  2 feet,  3 yards,  4 pounds. 

A compound  denominate  number  is  one  in  which  a quantity 
is  given  in  two  or  more  denominations  of  the  same  table  of 
measures;  as  3 yds.  2 ft.  6 in.,  or  3°  14'  30". 

Reduction  of  Denominate  Numbers. 

Reduction  of  denominate  numbers  consists  in  changing  them 
from  one  denomination  to  another  without  altering  their  value. 

Case  I. — To  reduce  from  a higher  to  a lower  denom- 
ination. 

Rule. — Multiply  the  quantity  in  the  highest  denomination 
by  the  number  of  times  a unit  of  this  denomination  contains  one 
of  the  next  lower,  and  to  the  product  add  the  quantity,  if  any,  in 
the  lower  denomination.  Proceed  in  like  manner  with  this 
result  and  continue  the  operation  until  the  desired  denomination 
is  reached. 

Case  II. — To  reduce  from  a lower  to  a higher  denom- 
ination. 

Rule. — Divide  the  given  quantity  by  the  number  of  times  a 
unit  of  its  denomination  is  contained  in  one  of  the  next  higher. 
Proceed  in  like  manner  with  the  quotient,  and  continue  the  oper- 
ation until  the  desired  denomination  is  reached.  The  last  quo- 
tient, with  the  several  remainders,  if  any,  annexed  in  order  will 
be  the  answer. 

Denominate  numbers  in  the  metric  system  are  reduced  by 
simply  moving  the  decimal  point  to  the  right  or  to  the  left. 

23 


24 


GUNNERY 


PROBLEMS. 

1.  Reduce  6 rds.  4 yds.  2 ft.  9 in.  to  inches.  Ans.  1,365  in. 

2.  Reduce  15|  hands  to  feet  and  inches.  Ans.  5 ft.  2 in. 

3.  Reduce  15°  25'  30"  to  seconds.  Ans.  55,530". 

4.  Reduce  8,589  " to  degrees  and  decimals  of  a degree.  Ans.  2° 

.386. 

5.  Reduce  40  cm.  to  inches  (approximately).  Ans.  16  in. 

6.  Reduce  50  kilos,  to  pounds  (legal  value).  Ans.  110.23  lbs. 

Addition  of  Compound  Denominate  Numbers. 

Rule. — Write  the  quantities,  placing  numbers  of  the  same 
denomination  in  the  same  column. 

Beginning  at  the  right  hand,  add  the  numbers  of  the  lowest 
denomination  and  divide  the  sum  by  the  number  of  units  of  this 
denomination  required  to  make  one  of  the  next  higher.  Write 
the  REMAINDER  Under  this  denomination  and  carry  the  quo- 
tient to  the  next  column. 

Add  the  column  of  each  denomination  in  the  same  way. 

PROBLEMS. 

1.  73°  42'  35" +8°  29'  52"  = what? 

Solution:  73°  42'  35" 

8°  29'  52" 

82°  12'  27"  Ans. 

35"+ 52"  = 87"  = 1' 27".  The  27"  is  written  in  the  seconds 
column  and  the  1'  is  carried  to  the  next  higher.  42'+29'+l' 
= 72'  = 1°  12'.  The  12'  is  written  in  the  minute  column  and 
the  1°  carried.  73°+8°  + l°  = 82°. 

2.  26°  31'  28"+31°  27'  43"  = what?  Ans.  57°  59'  11". 

3.  115°  57'  45"+9'  32"  = what?  Ans.  116°  7'  17". 

4.  lO^'*^  2^‘  10'"+7^’‘'^  1'*  7‘“  = what?  Ans.  18^''^^  l'*  5'“ 

5.  7“  6*^“  5'=“  4”“  + 9“  4*^“  6"“  7““  = what?  Ans.  17” 

j^dm  1”^*^ 

6.  M"'"*  3'’"  15‘^  8°"  + 2^"  13"^  12°"  14*^" +18"'"^ 

gqr  ^2'b  90^  10*^^  = what?  Ans.  2'  6'=^'  l*"^  Ih^^’  15°"  4‘^^ 


DENOMINATE  NUMBERS 


25 


Subtraction  of  Compound  Denominate  Numbers. 

Rule. — Write  the  subtrahend  under  the  minuend  so  that  num- 
bers of  the  same  denomination  may  be  in  the  same  column. 

Beginning  at  the  right  hand,  subtract  the  numbers  of  each 
denomination  separately  and  write  the  remainder  under  the 
numbers  subtracted. 

If  any  number  in  the  subtrahend  is  greater  than  the  number 
above  it  in  the  minuend,  borrow  a unit  from  the  next  higher  denom- 
ination of  the  minuend  and  reduce  it  to  the  next  lower  denomina- 
tion, add  this  to  the  number  in  the  minuend  to  be  subtracted  from, 
and  then  subtract. 

Proceed  in  the  same  way  with  each  denomination,  remember- 
ing that  a number  in  the  minuend  from  which  a unit  has  been 
borrowed  must  be  regarded  as  one  less  than  it  stands. 

PROBLEMS. 

1.  11°  14'  27"-7°  28'  14"  = what? 

Solution:  11°  14'  27" 

7°  28'  14" 

3°  46'  13"  Ans. 

27"  — 14"  = 13".  The  remainder  13"  is  written  under  the 
numbers  subtracted.  28'  is  greater  than  14'.  Borrowing 
1°  from  the  11°  of  the  minuend,  reducing  this  to  minutes  and 
adding  to  14'  we  have  74'.  74'  — 28' = 46'.  Remembering 

that  1°  has  been  borrowed  from  the  11°  we  have  10°  — 7°  = 3°. 

2.  63°  47'  28  "-15°  28'  13"  = what?  Ans.  48°  19'  15". 

3.  75°  36'  19  "-18°  29'  38"  = what?  Ans.  57°  6'  41". 

4.  43°  27'  15  "-19°  38'  17"  = what?  Ans.  23°  48'  58". 

5.  14^^^  12°^  9^^-6^'’  14°^  11'^^  = what?  Ans.  7'*'  13°"  14‘^h 

6.  85'’"2'’‘^5'**-58^"3'’‘^2‘'*R*  = what?  Ans.  26^"  3*’’^  2'"*  F* 

Multiplication  and  division  of  compound  denominate  num- 
bers may  be  performed  by  reducing  all  numbers  to  lowest 


26 


GUNNERY 


given  denomination,  performing  the  required  operation,  and 
then  reducing  the  result  to  any  higher  denomination  desired. 

This  method  of  performing  these  operations  will,  it  is 
thought,  be  sufficient  to  meet  the  wants  of  gunners  in  ordinary 
cases. 


CHAPTER  VI 


RATIO  AND  PROPORTION 

A ratio  is  the  measure  of  the  relation  of  one  quantity  to 
another  of  the  same  kind  and  denomination.  It  is  found  by 
dividing  the  first  quantity  by  the  second,  and  is  always  an 
abstract  number.  Thus,  the  ratio  of  8 ft.  to  4 ft.  is  2. 

The  sign  of  ratio  is  : , which  is  read  “is  to.”  Thus:  the 
ratio  of  8 to  4 is  written  8 : 4,  read  “8  is  to  4,”  and  equals 
8-^4,  or  2. 

A simple  ratio  is  the  ratio  of  two  quantities.  Each  quan- 
tity is  called  a term  of  the  ratio. 

A proportion  is  a comparison  of  equal  ratios. 

The  sign  of  proportion  is  , which  is  read  “as”. 

A simple  proportion  is  a comparison  of  two  equal  simple 
ratios.  Thus:  3 : 6::  8 : 16,  which  is  read  ‘‘3  is  to  6 as  S is  to 
16.” 

Each  quantity  in  a proportion  is  called  a term.  The  1st 
and  4th  terms  are  called  the  extremes;  the  2d  and  3d,  the 
means. 

In  any  proportion  the  product  of  the  extremes  is  equal  to 
the  product  of  the  means.  Hence  either  extreme  is  equal  to  the 
product  of  the  means  divided  by  the  other  extreme,  and 
either  mean  is  equal  to  the  product  of  the  extremes  divided  by 
the  other  mean. 

Simple  proportion  is  employed  when  three  terms  are  given 
to  find  a fourth.  Two  of  the  three  terms  must  be  of  the  same 
denomination  and  the  other  of  the  same  as  that  to  be  found. 
The  rule  by  which  the  fourth  term  is  found  is  often  called  the 
single  rule  of  three. 


27 


28 


GUNNERY 


Rule. — For  the  3rd  term,  write  that  quantity  which  is  of  the 
same  denomination  as  that  to  he  found.  For  the  2d  term  write 
the  greater  of  the  other  two  quantities  when  the  4th  term  is  to  he 
greater  than  the  3d;  or  the  less,  when  the  4th  term  is  to  he  less  than 
the  3d.  Then  divide  the  product  of  the  2d  and  3d  terms  hy  the  1st; 
the  quotient  will  he  the  required  4th  term. 

If  the  1st  and  2d  terms  are  quantities  of  the  same  kind, 
but  of  different  denominations,  they  must  be  reduced  to  the 
same  denomination. 

If  the  3d  term  is  a compound  denominate  number,  it 
must  be  reduced  to  the  lowest  given  denomination. 

PROBLEMS. 

1.  If  6 paces  equal  5 yds.,  how  many  paces  in  100  yds.? 
Ans.  120  paces. 

2.  If  1 kilo,  equals  2i  lbs,  how  many  lbs.  in  50  kilos.? 
Ans.  110  lbs. 

3.  If  1 mm.  equals  ^ in.,  how  many  inches  in  75  mm.? 
Ans.  3 in. 

4.  If  1 cm.  equals  .3937  in.,  how  many  inches  in  15  cm.? 
Ans.  5.91  in. 

5.  If  1 m.  equals  39.37  in., how  many  meters  in  1,000  yds.? 
Ans.  914.4  m. 

6.  If  1 Km.  equals  f mi.,  how  many  yards  in  5 Km.? 
Ans.  5,500  yds. 


CHAPTER  VII 


PERCENTAGE 

Per  cent,  means  hy  the  hundred. 

The  sign  of  per  cent,  is  %,  which  is  read  “per  cent.”  Thus: 
4%  is  read  “4  per  cent.”  and  means  ifo,  or  .04. 

Percentage  is  the  result  obtained  by  taking  a given  per 
cent.,  or  so  many  hundredths  of  a given  number. 

The  given  per  cent.,  or  number  of  hundredths  taken,  is 
called  the  rate. 

The  number  on  which  the  percentage  is  estimated  is  called 
the  base. 

The  base  plus  the  percentage  is  called  the  amount. 

The  relation  between  the  base,  rate,  and  percentage  is 
such  that,  any  two  of  them  being  given,  the  third  can  be  found. 
Three  cases  may  arise. 

Case  I. — Given  the  base  and  rate,  required  the  per- 
centage. 

Rule. — Multiply  the  base  by  the  rate  expressed  decimally, 
the  product  will  be  the  percentage. 


PROBLEMS. 

1.  35%  of  160  = what? 

Solution:  160  X .35  = 56,  Ans. 

2.  5%  of  1,900  = what?  Ans.  95. 

3.  62^%  of  1,664  = what?  Ans.  1,040. 

4.  15f%of  576  = what?  Ans.  90. 

29 


30 


GUNNERY 


Case  II. — Given  the  base  and  percentage,  required 

THE  RATE. 

Rule. — Divide  the  'percentage  by  the  base,  the  quotient  will 
be  the  rate. 

PROBLEMS. 

1.  9 is  what  % of  45? 

Solution:  A = i = ==20%,  Ans. 

2.  95  is  what  % of  1,900?  Ans.  5%. 

3.  2 is  what  % of  15?  Ans.  13|%. 

4.  5.12  is  what  % of  640?  Ans.  f%. 

Case  III. — Given  the  rate  and  percentage,  required 

THE  BASE. 

Rule. — Divide  the  percentage  by  the  rate  expressed  decimally, 
the  quotient  will  be  the  base. 

1.  95  is  5%  of  what? 

Solution:  .^  = 1,900,  Ans. 

2.  3.80  is  5%  of  what?  Ans.  76. 

3.  19.20  is  tV%  of  what?  Ans.  3,200. 

4.  189.8  is  104%  of  what?  Ans.  182.5. 


CHAPTER  VIII 


POWERS  AND  ROOTS 

A power  of  a quantity  is  either  the  quantity  itself  or  some 
product  of  the  quantity  by  itself.  The  quantity  so  multi- 
plied is  called  the  root  of  the  power. 

Powers  are  named  according  to  the  number  of  times  the 
quantity  is  multiplied;  this  is  indicated  by  a small  figure 
called  an  exponent,  written  to  the  right  of  and  above  the  quan- 
tity. Thus  2^  is  the  first  power  of  2 ; 2^  = 2 X 2 = 4,  is  the  second 
power,  or  square,  of  2;  2^  = 2X2X2  = 8,  the  third  power,  or 
cube  of  2;  and  so  on. 

The  exponent  1 is  ordinarily  omitted,  and  when  no  expo- 
nent is  written  1 is  understood. 

Roots  are  named  according  to  the  number  of  the  times  they 
enter  a given  power  as  a factor;  this  is  indicated  by  what  is 
called  the  radical  sign,  V , or  by  a fractional  exponent. 

When  the  radical  sign  is  used,  a small  figure,  called  an 
index,  is  placed  over  the  sign  to  show  the  name  of  the  root 
if  any  other  than  the  second,  or  square,  root  is  to  be  indicated. 
Thus:  V4  indicates  the  square  root  of  4;  "5' 27,  the  third,  or 
cube,  root  of  27 ; ^ 32,  the  fifth  root  of  32.  When  no  index  is 
written,  the  index  2 is  always  understood. 

When  a fractional  exponent  is  used,  the  numerator  indicates 
a power;  the  denominator,  a root.  Thus,  4^indicates  the  first 
power  and  square  root  of  4;  8^  the  second  power  of  8 and  the 
cube  root  of  the  result. 

VTien  a root  of  a quantity  can  be  found  exactly,  the  latter 
is  called  a perfect  power  of  this  root;  when  it  can  not  be  found 
exactly,  an  imperfect  power.  Thus:  8 is  a perfect  third  power 

31 


32 


GUNNERY 


whose  cube  root  is  2;  an  imperfect  second  power,  since  its  square 
root  is  2.8284271 +. 

Squaee  Root. 

The  first  ten  numbers  and  their  squares  are — 

Numbers:  1234567  89  10 

Squares:  1 4 9 10  25  36  49  64  81  100 

From  this  it  is  evident  that  the  square  root  of  any  perfect 
square,  expressed  by  two  figures,  will  be  expressed  by  a single 
figure. 

Case  I. — To  find  the  squaee  eoot  of  any  whole  num- 

BEE  OE  DECIMAL. 

Rule. — Separate  the  number  into  periods  of  two  figures  each, 
commencing  at  units  or  at  the  decimal  point. 

Find  the  greatest  perfect  square  in  the  first  period  on  the  left; 
place  its  root  on  the  right,  like  a quotient  in  division;  then  sub- 
tract the  square  from  the  period  and  to  the  remainder  bring  down 
the  next  period  for  a dividend. 

Double  the  root  figure  found  and  place  it  on  the  left  for  a trial 
divisor;  find  how  often  this  is  contained  in  the  dividend,  exclusive 
of  the  right-hand  figure,  and  annex  the  quotient  to  the  root  and 
to  the  divisor;  multiply  the  completed  divisor  by  the  quotient,  sub- 
tract the  product  from  the  dividend,  and  to  the  remainder  bring 
down  the  next  period  as  before. 

Double  the  whole  root  found  for  a new  trial  divisor,  and  pro- 
ceed as  before  until  all  the  periods  have  been  brought  down. 

If  any  trial  divisor  be  greater  than  its  dividend,  the  cor- 
responding figure  of  the  root  will  be  0. 

If  the  product  of  a trial  divisor  by  a figure  of  the  root  be 
greater  than  the  corresponding  dividend,  the  figure  of  the  root 
is  too  large. 

If  the  number  is  not  a perfect  square,  there  will  be  a remain- 
der after  all  the  periods  have  been  brought  down.  In  this 


POWERS  AND  ROOTS 


33 


case,  periods  of  two  O’s  each  may  be  annexed  and  the  operation 
continued  until  any  desired  decimal  order  of  the  root  is  reached. 

If  the  number  contains  an  odd  number  of  decimal  places, 
add  a 0. 

Case  II. — To  find  the  square  root  of  a common  frac- 
tion. 

Rule. — Find  the  square  roots  of  the  numerator  and  denomi- 
nator separately  if  both  are  perfect  squares;  if  either  is  not,  reduce 
the  fraction  to  a decimal  and  find  the  square  root  of  this. 


PROBLEMS. 


V 730.05  = what?  1.  Vl,444=what?  Ans.  38. 


Solution: 


730.05)27.019-1-,  Ans.  2.  V 118.81  = what?  Ans.  10.9. 


4 


3.  V 164,998.44  = what?  Ans.  406.2. 


5,401)10,500 


47)330 


329 


4.  V272x^  = what?  Ans.  16J. 

5.  V|=what?  Ans.  .9258+. 

6.  V 61  = what?  Ans.  2.5298+. 


5,401 

54,029)509,900 


486,261 

23,639,  remainder. 


CHAPTER  IX 


GEOMETRICAL  MAGNITUDES 

A geometrical  magnitude  is  a quantity  that  has  either 
length,  breadth,  thickness  or  form. 

There  are  four  kinds  of  geometrical  magnitudes : lines,  sur- 
faces, solids,  and  angles.  A point  has  position,  but  not  mag- 
nitude. 

Some  of  the  subdivisions  of  these  magnitudes  are  as  follows : 

Lines. 

A line  is  a magnitude  that  has  length  only. 

A straight  line  is  a line  that  does  not  change  direction  at 
any  point. 

A curved  line  is  a line  that  changes  direction  at  every  point. 

A straight  line  is  ordinarily  called  a right  line,  or  simply  a 
line;  a curved  line,  a curve. 

[For  simplicity,  the  following  definitions  regarding  sur- 
faces and  angles  are  here  given: 

A surface  is  a magnitude  that  has  length  and  breadth,  but 
not  thickness. 

A plane  surface,  or  plane,  is  a surface  in  which  a straight 
line,  joining  any  two  points  in  the  surface,  vdll  wholly  lie. 

A plane  angle,  or  an  angle,  as  before  defined,  is  the  opening 
between  two  straight  lines  which  meet  at  a point;  as  a magni- 
tude it  has  form,  but  neither  length,  breadth,  nor  thickness. 

A right  angle  is  an  angle  measured  by  90°.] 

Parallel  lines  are  lines,  in  the  same  plane,  which  would  not 

34 


GEOMETRICAL  MAGNITUDES 


35 


meet  however  far  either  way  both  of  them  might  be  extended; 
as  the  lines  AB,  CD.  (Fig.  2.) 


A B 

C D 

Fig.  2. 


Perpendicular  lines  are  straight  lines  at  right  angles  to 
each  other;  as  the  lines  AB,  CD.  (Fig.  3.) 


-B 


Jb 

Fig.  3. 


A vertical  line  is  one  that  points  toward  the  center  of  the 
earth.  A plummet  is  ordinarily  used  to  determine  this  direc- 
tion. 

A horizontal  line  is  one  at  right  angles  to  a vertical  line.  It 
is  parallel  to  the  horizon,  or  sea  level,  and  may  be  determined 
by  means  of  a plummet  and  carpenter’s  square  or  by  a car- 
penter’s level. 


Angles. 

An  acute  angle  is  one  that  is  less  than  a. right  angle;  as  the 
angle  BAC.  (Fig.  4.) 


Fig.  4. 


36 


GUNNERY 


An  obtuse  angle  is  one  that  is  greater  than  a right  angle;  as 
the  angle  CAB.  (Fig.  5.) 


A B 

Fig.  5. 


When  one  straight  line  intersects  another  the  four  angles 
formed  are  named  according  to  their  relative  positions,  thus: 
Adjacent  angles  are  the  two  angles  on  the  same  side  of 
either  line;  as  the  angles  AOC  and  COB  are  adjacent. 


Opposite  angles  are  either  pair  of  those  which  point  in  oppo- 
site directions;  as  AOD  and  COB. 

When  one  straight  line  intersects  two  parallel  lines  the 
angles  within  the  parallels  on  different  sides  of  the  intersecting 
line,  but  not  adjacent,  are  called  alternate  angles;  as  AHG 
and  HGD. 


Fig.  7. 


An  interior  angle  is  an  angle  formed  inside  of  an  inclosed 
figure  by  the  meeting  of  two  of  its  sides;  as  ABC. 


GEOMETRICAL  MAGNITUDES 


37 


An  exterior  angle  is  an  angle  formed  outside  the  figure  by 
any  side  and  the  prolongation  of  an  adjacent  side;  as  aAB. 


A reentering  angle  is  one  that  points  inward,  as  ADC;  a 
salient  angle,  one  that  points  outward,  as  ABC. 

Surfaces. 

A curved  surface  is  a surface  no  part  of  which  is  a plane. 

A polygon  is  a plane  surface  bounded  by  straight  lines. 

A regular  polygon  is  one  whose  sides  are  equal. 

Polygons  are  named  according  to  the  number  of  their 
sides;  one  of  three  sides  is  a triangle;  of  four,  a quadrilateral; 
of  five,  a pentagon;  of  six  a hexagon;  and  so  on. 

The  following  diagrams  represent  regular  polygons: 


POLYGONS 


Triaugler  Square.  Hexagon.  Octagon. 

Fig.  9. 


A diagonal  of  a polygon  is  a straight  line  joining  any  two 
angles  not  adjacent. 

The  hase  is  the  side  on  which  the  polygon  stands. 

The  altitude  is  the  perpendicular  distance  from  the  base  to 
the  highest  point,  or  one  of  the  highest  points,  of  the  polygon. 
The  perimeter  of  a polygon  is  its  bounding  line. 


38 


GUNNERY 


Triangles. — Triangles  are  classified  according  to  the  rela- 
tive lengths  of  their  sides,  and  also  according  to  the  nature  of 
their  angles. 

A scalene  triangle  has  no  two  sides  equal;  an  isosceles  tri- 
angle has  two,  and  only  two,  sides  equal;  and  an  equilateral 
triangle  has  three  sides  equal. 

An  acute-angled  triangle  has  three  acute  angles;  an  ohtuse- 
angled  triangle,  one  obtuse  angle;  a right-angled  triangle,  one 
right  angle.  In  a right-angled  triangle  the  side  opposite  the 
right  angle  is  called  the  hypotenuse;  the  other  sides,  the  base 
and  the  perpendicular. 


ACUTE-ANGLED  TKIANGLES. 


Scalcao.  Isosceles  EquIlateraL 
OBTUSE-ANGLED  TEIANCJLES.  EIGHT- ANGLED  TRIANGLESi 


Scalene,  Isosceles.  Scalene.  Isosceles. 

Fig.  10. 


Quadrilaterals. — Quadrilaterals  are  classified  according 
to  the  relative  directions  of  their  sides. 

A trapezium  has  no  two  sides  parallel;  a trapezoid  has  two, 
and  only  two,  sides  parallel;  a parallelogram  has  two  pairs  of 
parallel  sides. 

Parallelograms  are  classified  according  to  the  nature  of  their 
angles. 

A rhomboid  is  a parallelogram  with  no  right  angle;  a rec- 
tangle, one  with  four  right  angles. 

A rhombus  is  an  equilateral  rhomboid;  a square,  an  equi- 
lateral rectangle. 


GEOMETRICAL  MAGNITUDES 


39 


Circles. — A circle  is  a plane  surface  bounded  by  a curved 
line  every  point  of  which  is  equally  distant  from  a point  within, 
called  the  center. 

A circumference  is  the  curved  bounding  line  of  a circle. 


TRAPEZimiL  TRAPEZOID.,  PARALLELOGRAMS. 


Ebomboid.  Rhombus.  Rectangle.  Square. 

Fig.  11. 


A diameter  of  a circle  is  any  straight  line  drawn  through  the 
center  and  ending  each  way  in  the  circumference. 


Fig.  12. 


A radius  of  a circle  is  any  straight  line  drawn  from  the 
center  to  the  circumference. 

An  arc  of  a circle  is  any  portion  of  the  circumference;  a 
chord  of  an  arc  is  the  straight  line  which  joins  its  extremities. 


Solids. 

A solid  is  a magnitude  that  has  length,  breadth  and  thick- 
ness. It  may  have  plane  or  curved  bounding  surfaces,  or 
both.  If  the  bounding  surfaces  are  planes,  they  are  called 
the  faces  of  the  solid,  and  the  lines  of  intersection  of  the  faces 
are  called  the  edges. 


40 


GUNNERY 


A prism  is  a solid  having  two  of  its  faces  equal  and  parallel 
polygons  and  the  other  faces  parallelograms.  The  parallel 
polygons  . are  called  bases;  and  the  perpendicular  distance 
between  them  the  altitude  of  the  prism.  The  parallelograms 
are  called  lateral  faces,  and  when  taken  together  they  constitute 
the  convex  surface  of  the  prism. 

When  all  the  lateral  faces  are  rectangles,  the  prism  is 
called  a right  prism;  when  some  are  rhomboids,  an  oblique 
prism. 

Prisms  are  named  according  to  the  form  of  their  bases,  as 
triangular,  quadrangular,  pentangular,  hexangular,  etc. 

When  the  bases  and  faces  of  a prism  are  squares,  the  prism 
is  called  a cube. 

When  the  bases  of  a prism  are  circles,  or  regular 
polygons  of  an  infinite  number  of  sides,  the  prism  is  called 
a cylinder.  When  a perpendicular  through  the  center  of  one 
base  also  passes  through  the  center  of  the  other,  a cylinder 
is  called  a right  cylinder;  when  it  does  not,  an  oblique  cylinder. 


(trlaiigalan  QnadraDgalar.  Hssangular. 

Fig.  13. 


A pyramid  is  a solid  having  for  one  of  its  faces  any  polj'gon 
and  for  the  others  triangles  which  meet  at  a common  point. 

The  polygon  is  called  the  base;  the  triangles,  the  lateral 
faces;  and  the  point  at  which  the  triangles  meet,  the  vertex. 
The  perpendicular  distance  from  the  vertex  to  the  plane  of 
the  base  is  called  the  altitude.  The  lateral  faces  taken  together 
constitute  the  convex  surface. 

A right  pyramid  is  one  whose  base  is  a regular  polygon  and 
whose  lateral  faces  are  isosceles  triangles.  In  this  case  the 


GEOMETRICAL  MAGNITUDES 


41 


perpendicular  from  the  vertex  to  the  plane  of  the  base  passes 
through  the  center  of  the  base,  and  is  called  the  axis  of  the 
P3U’amid;  and  a perpendicular  from  the  vertex  to  any  side  of 
the  base  passes  through  the  middle  of  the  side,  and  is  called 
the  slant  height  of  the  pyramid. 

Pyramids  are  named  according  to  the  shape  of  their  bases, 
as  triangular,  quadrangular,  pentangular,  hexangular,  etc. 

When  the  base  of  a pyramid  is  a circle,  or  regular  polygon 
of  an  infinite  number  of  sides,  the  pyramid  is  called  a cone. 
When  a perpendicular  from  the  vertex  to  the  plane  of  the  base 
passes  through  the  center  of  the  base,  the  cone  is  a right  cone, 
and  its  slant  height  is  the  distance  from  the  vertex  to  the  cir- 
cumference of  the  base. 


Triangulat 


PYEAMIDS 


Cone. 


A frustum  of  a pyramid  or  cone  is  the  portion  which  remains 
when  the  top  is  cut  off  by  a plane  parallel  to  the  base.  The 
altitude  of  a frustum  is  the  perpendicular  distance  between 
its  parallel  bases. 

The  slant  height  and  axis  of  a frustum  of  a right  pyramid 
or  right  cone  are  the  portions  of  the  slant  height  or  axis  of 


FRUSTUMS 


, ,'aadrangular. 

Fig.  15. 


Conical. 


the  pyramid  or  cone  included  between  the  bases  of  the  frus- 
tum. 

Frustums  are  named  according  to  the  shape  of  their 


42 


GUNNERY 


bases,  as  triangular,  quadrangular,  hexangular,  octangular, 
conical. 

Spheres — A sphere  is  a solid  bounded  by  a curved  surface 
every  point  of  which  is  equally  distant  from  a point  within 
called  the  center.  A diameter  of  a sphere  is  a straight  hne 

SPHERE 


passing  through  the  center  and  ending  each  way  in  the  surface; 
a radius  is  a straight  line  drawn  from  the  center  to  any  point 
of  the  surface. 

Every  section  of  a sphere  by  a plane  is  a circle;  any  section 
by  a plane  through  the  center  is  called  a great  circle. 


CHAPTER  X 


MENSURATION 

Mensuration  is  the  art  of  computing  lengths,  areas,  and 
volumes  of  geometrical  magnitudes  by  arithmetical  rules. 

A length  is  a definite  portion  of  a line  in  terms  of  its  unit 
of  measure;  an  area,  that  of  a surface;  a volume,  that  of  a solid. 

The  unit  of  measure  of  a surface  is  a square;  of  a volume, 
a cube. 

LENGTHS. 

Sides  of  a right-angled  triangle. 

I.  — To  FIND  HYPOTENUSE  WHEN  BASE  AND  PERPENDICULAR 
ARE  GIVEN. 

Rule. — Add  the  squares  of  base  and  perpendicular  and 
extract  square  root  of  the  sum. 

II.  — To  FIND  BASE  OR  PERPENDICULAR  WHEN  THE  HYPOT- 
ENUSE AND  EITHER  SIDE  ARE  GIVEN. 

Rule. — From  the  square  of  hypotenuse  subtract  the  square 
of  the  given  side  and  extract  the  square  root  of  the  remainder. 

PROBLEMS. 

1.  Base  equals  4.8  ft.;  perpendicular,  3.6  ft.;  what  is 
hypotenuse?  Ans.  6 ft. 

2.  Base  equals  15  yds.;  perpendicular,  9 yds.  1 ft.;  what 
is  hypotenuse?  Ans.  17  yds.  2 ft. 

3.  Hypotenuse  equals  67.43  yds.;  perpendicular,  52.6; 
what  is  the  base?  Ans.  42.17+. 

4.  Hypotenuse  equals  52.32  ft.;  base,  32.11;  what  is  per- 
pendicular? Ans.  41.30+. 


43 


44 


GUNNERY 


Lines  of  a Circle. 

The  ratio  of  the  circumference  of  a circle  to  the  diameter 
is  3. 1415926 +,  which  ratio  is  represented  by  the  Greek  letter 
called  pi. 

I.  — To  FIND  THE  CIRCUMFERENCE  WHEN  THE  DIAMETER  IS 
GIVEN. 

Rule. — Multiply  the  diameter  hy  3.1416. 

II.  — To  FIND  THE  DIAMETER  WHEN  THE  CIRCUMFERENCE 
IS  GIVEN. 

Rule. — Divide  the  circumference  hy  3.1416. 

PROBLEMS. 

1.  Diameter  equals  3.2  in.;  what  is  the  circumference? 
Ans.  10.05  in. 

2.  Diameter  equals  1 ft.  3 in.;  what  is  the  circumference? 
Ans.  3 ft.  11.12  in. 

3.  Circumference  equals  63.9  ft.;  what  is  the  diameter? 
Ans.  20.34  ft. 

4.  Circumference  equals  6 yd.  1 ft.  4 in. ; what  is  the  diam- 
eter in  feet?  Ans.  6.154  ft. 

Areas. 

Triangle. 

I.  — To  FIND  AREA  WHEN  BASE  AND  ALTITUDE  ARE  GIVEN. 
Rule. — Multiply  the  base  hy  half  the  altitude. 

II.  — To  FIND  AREA  WHEN  THREE  SIDES  ARE  GI^rEN. 

Rule. — From  half  the  sum  of  the  three  sides  subtract  each 
side  separately;  multiply  the  half  sum  and  three  remainders 
together,  and  extract  the  square  root  of  the  product. 


MENSURATION 


45 


PROBLEMS. 

1.  Base  equals  4.75  ft.;  altitude,  3.5  ft.;  what  is  area? 
Ans.  8.312  sq.  ft. 

2.  Base  equals  2 ft.  7 in. ; altitude,  2 ft.  5 in. ; what  is  area? 
Ans.  3.12  sq.  ft. 

3.  Sides  equal  3 ft.,  4 ft.,  and  5 ft.;  what  is  area?  Ans. 
6 sq.  ft. 

4 Sides  equal  1 ft.  10  in.,  2 ft.,  and  3 ft.  2 in.;  what  is 
area?  Ans.  1 sq.  ft.  101.9  sq.  in. 

Parallelogram. 

To  FIND  AREA  WHEN  BASE  AND  ALTITUDE  ARE  GIVEN. 
Rule. — Multiply  the  base  by  the  altitude. 

PROBLEMS. 

1.  Base  equals  9 ft.  4 in. ; altitude,  2 ft.  5 in. ; what  is  area? 
Ans.  22.5  sq.  ft. 

2 Base  equals  2 yds.  2.25  ft.;  altitude  5 ft.  9 in.;  what  is 
area  in  square  feet?  Ans.  47.4375  sq.  ft. 

Trapezoid. 

To  FIND  AREA  WTIEN  PARALLEL  SIDES  AND  PERPENDICULAR 
DISTANCE  BETWEEN  THEM  ARE  GIVEN. 

Rule — Multiply  half  the  sum  of  parallel  sides  by  the  per- 
pendicular distance. 


PROBLEMS. 

1.  Parallel  sides  equal  2.25  ft.  and  2.75  ft.;  perp.  dist., 
2.5  ft.;  what  is  area?  Ans.  6.25  sq.  ft. 

2.  Parallel  sides  equal  3 ft.  5 in.,  and  2 ft.  7 in.;  perp.  dist. 
2 ft.  8 in. ; what  is  area?  Ans.  8 sq.  ft. 


46 


GUNNERY 


Circle. 

I.  — To  FIND  AREA  WHEN  DIAMETER  AND  CIRCUMFERENCE 
ARE  GIVEN. 

Rule. — Multiply  the  diameter  hy  one-fourth  of  the  circum- 
ference. 

II.  — To  FIND  AREA  WHEN  THE  DIAMETER  IS  GIVEN. 

Rule. — Multiply  the  square  of  the  diameter  hy  .1851^. 

III.  — To  FIND  AREA  WHEN  THE  RADIUS  IS  GIVEN. 

Rule. — Multiply  the  square  of  the  radius  hy  3.14-16. 

PROBLEMS. 

1.  Diameter  equals  22j  ft.,  circumference  69.9  ft.;  what 
is  area?  Ans.  388.82  sq.  ft. 

2.  Diameter  equals  2 ft.  5 in.,  circumference  7 ft.  7 in.; 
what  is  area?  Ans.  4 sq.  ft.  83.75  sq.  in. 

3.  Diameter  equals  3.2  inches;  what  is  the  area?  Ans. 
8.042  sq.  in. 

4.  Diameter  equals  1 ft.  3 in.;  what  is  the  area?  Ans. 
1.227  sq.  ft. 

5 Radius  equals  5 in.;  what  is  the  area?  Ans.  78.54  sq. 
in. 

6.  Radius  equals  2.25  in.;  what  is  the  area?  Ans.  15.9 
sq.  in. 

Convex  Surface,  Right  Prism,  or  Cylinder. 

To  FIND  AREA  WHEN  PERIMETER  OF  BASE  AND  ALTITUDE 
ARE  GIVEN. 

Rule. — Multiply  perimeter  of  base  hy  the  altitude. 


MENSURATION 


47 


PROBLEMS. 

1.  The  sides  of  base  of  a right  prism  equal  5|,  6|,  8f,  9, 
and  10  in.,  the  altitude  llj  in.;  what  is  area  of  convex  surface? 
Ans.  3 sq.  ft.  12.375  sq.  in. 

2.  The  diameter  of  a right  cylinder  equals  1 ft.  2|  in., 
the  altitude  1 ft.  9 in.;  what  is  area  of  convex  surface?  Ans. 
6 sq.  ft.  92.6  sq.  in. 

Convex  Surface,  Right  Pyramid,  or  Cone. 

To  FIND  AREA  WHEN  PERIMETER  OF  BASE  AND  SLANT  HEIGHT 
ARE  GIVEN. 

Rule. — Multiply  sum  of  'perimeter  of  bases  by  one-half  the 
slant  height. 

PROBLEMS. 

1.  Each  side  of  a triangular  pyramid  equals  3 ft.  6 in., 
the  slant  height  18  ft.;  what  is  area  of  convex  surface?  Ans. 
94.5  sq.  ft. 

2.  The  diameter  of  the  base  of  a conical  tent  equals  16 
ft.,  the  altitude  14  ft.;  how  many  square  yards  of  canvas  in 
the  tent?  Ans.  45.016  sq.  yds. 

Convex  Surface,  Frustum,  Right  Pyramid,  or  Cone. 

To  FIND  AREA  WHEN  PERIMETERS  OF  BASES  AND  SLANT 
HEIGHT  ARE  GIVEN. 

Rule. — Multiply  sum  of  perimeters  of  bases  by  one-half  the 
slant  height. 

PROBLEMS. 

Each  side  of  lower  base  of  a frustum  of  a quadrangular 
pjrramid  equals  10  in.,  of  upper  base  9 in.,  the  slant  height 
20  in. ; what  is  area  of  convex  surface?  Ans.  5 sq.  ft.  40  sq.  in. 

2.  The  circumferences  of  the  bases  of  a frustum  of  a 
right  cone  are  22  in.  and  15.71  in.,  the  slant  height  26  in.; 
what  is  area  of  convex  surface?  Ans.  3 sq.  ft.  58.23  sq.  in. 


48 


GUNNERY 


Surface  of  Sphere. 

The  surface  of  a sphere  equals  four  great  circles. 

To  FIND  AREA  WHEN  DIAMETER  IS  GIVEN. 

Rule. — Multiply  the  square  of  the  diameter  by  3.1416. 

PROBLEMS. 

Diameter  of  sphere  equals  10  in.;  what  is  area  of  sur- 
face? Ans.  314.16  sq.  in. 

2.  Diameter  of  sphere  equals  1 ft.  3 in.;  what  is  area  of 
surface?  Ans.  4.91  sq.  ft. 

Volumes. 

Prism  or  Cylinder. 

To  FIND  volume  when  AREA  OF  BASE  AND  ALTITUDE  ARE 
GIVEN. 

Rule. — Multiply  the  area  of  the  base  by  the  altitude. 


PROBLEMS. 

1.  The  edges  of  the  base  of  a rectangular  prism  equal  2.2 
in.  and  1.1  in.,  the  altitude  3.3  in.;  what  is  the  volume?  Ans. 
7.986  cu.  in. 

2.  The  edges  of  the  base  of  a triangular  prism  equal  3 ft., 
4 ft.,  and  5 ft.,  the  altitude  10  ft.;  what  is  the  volume?  Ans. 
60  cu.  ft. 

3.  The  diameter  of  base  of  a cylinder  equals  1 ft.  3 in., 
the  altitude  2 ft.  6 in.;  what  is  the  volume?  Ans.  3.067  cu.  ft. 

4.  The  circumference  of  the  base  of  a cylinder  equals 
3.1416  ft.,  the  altitude  3 ft.  9 in.;  what  is  the  volume?  Ans. 
2.945  cu.  ft. 


MENSURATION 


49 


Right  Pyramid  or  Cone. 

To  FIND  VOLUME  WHEN  AREA  OF  BASE  AND  ALTITUDE  ARE 
GIVEN. 

Rule. — Multiply  the  area  of  the  hose  by  one-third  of  the 
altitude. 

PROBLEMS. 

1.  Each  edge  of  the  base  of  a right  rectangular  pyramid 
equals  2.5  ft.,  the  altitude  2.25  ft.;  what  is  the  volume?  Ans. 
4.6875  cu.  ft. 

2.  The  radius  of  the  base  of  a cone  equals  5 ft.,  the  alti- 
tude 21  ft.;  what  is  the  volume?  Ans.  549.78  cu.  ft. 

Frustum,  Right  Pyramid,  or  Cone. 

To  FIND  VOLUME  WHEN  AREA  OF  BASES  AND  ALTITUDE  ARE 
GIVEN. 

Rule. — To  the  sum  of  the  two  bases  add  the  square  root  of 
their  product,  and  multiply  the  result  by  one-third  of  the  altitude. 

PROBLEMS. 

1.  Each  edge  of  the  lower  base  of  a frustum  of  a right 
quadrangular  pyramid  equals  3 ft.,  of  the  upper  base  2 ft., 
the  altitude  15  ft.;  what  is  the  volume?  Ans.  95  cu.  ft. 

2.  The  diameters  of  the  bases  of  a frustum  of  a cone  equal 
18  in.  and  10  in.,  the  altitude  16  in.,  what  is  the  volume?  Ans. 
2,530.03  cu.  in. 

Sphere. 

To  FIND  VOLUME  WHEN  DIAMETER  IS  GIVEN. 

Rule. — Multiply  the  cube  of  the  diameter  by  .5236. 

PROBLEMS. 

1.  The  diameter  of  a sphere  equals  10  in.;  what  is  the 
volume?  Ans.  523.6  cu.  in. 

2.  The  diameter  of  a sphere  equals  15  in.;  what  is  the 
volume?  Ans.  1.0227  cu.  ft. 


CHAPTER  XI 


ALGEBRAIC  EXPRESSIONS  AND  SIMPLE 
EQUATIONS 

Algebeaic  Expkessions. 

An  algebraic  expression  is  a mathematical  statement  in 
which  the  quantities  considered  are  represented  by  letters  and 
the  operations  to  be  performed  are  indicated  by  signs. 

The  quantities  may  be  either  known  or  unknown.  Known 
quantities  are  usually  represented  by  the  first  letters  of  an 
alphabet;  as  a,  b,  c;  a',  b',  c',  read  “a  prime,  b prime,  c prime”; 
a",  b",  c",  read  '‘a  second,  b second,  c second”;  ai,  bi,  Ci,  read 
“a  sub  one,  b sub  one,  c sub  one,”  etc.  Unknown  quantities 
are  usually  represented  by  the  last  letters  of  an  alphabet;  as 
X,  y,  z;  x',  y',  z';  Xi,  yi,  zp,  Xo,  yo,  Zo,  read  “x  sub  zero,  y sub  zero, 
z sub  zero,”  etc. 

The  signs  are  the  same  as  those  used  in  arithmetic. 

Quantities  multiplied  together  are  called  factors  of  their 
product.  When  factors  are  letters,  the  sign  of  multiplication 

, , . . , a c . . ac 

IS  omitted;  as  aXbXc  is  written  abc;  7X3  is  WTitten  73; 

b d bd 

aXaXaXaXbXbXbXcXcXd,  is  wTitten  a*¥c-d  and  is  read 

“a  fourth,  b cube,  c square,  d.” 

A coefficient  is  usually  a number  wTitten  before  a quantity 
expressed  by  letters  to  show  how  many  times  the  quantity 
is  to  be  taken  additively.  Thus:  in  24a5,  24  is  the  coefficient 
of  ab,  and  shows  that  ab  is  taken,  additively,  24  times. 

50 


ALGEBRAIC  EXPRESSIONS  AND  SIMPLE  EQUATIONS  51 


When  the  quantity  expressed  by  letters  represents  both 
known  and  unknown  quantities,  the  product  of  the  numerical 
coefficient  and  letters  representing  the  known  quantities  is 
usually  considered  as  the  coefficient.  Thus:  in  7 ax,  7a  is 
regarded  as  the  coefficient  of  a;  or  7 may  be  regarded  as  the 
coefficient  of  ax. 

When  no  coefficient  is  expressed,  the  coefficient  1 is  always 
understood.  Thus:  ahc  means  the  same  as  la6c. 

A term  is  an  algebraic  expression  whose  parts  are  not  sep- 
arated by  a plus  or  a minus  sign.  Thus : Zax,  bhy,  and  3ax  -f-  5hy 
are  terms.  In  2x-  — 3ax+4:C‘^,  2x‘^  — Sax,  and  -f  4c^,  are,  respec- 
tively, the  1st,  2d,  and  3d  terms. 

Terms  in  algebraic  expressions,  like  numbers  in  arithmetic, 
are  divided  into  positive  terms,  or  terms  to  be  added  together, 
and  negative  terms,  or  terms  to  be  subtracted  from  positive 
terms,  but  added  to  negative  terms.  Positive  terms  are  pre- 
ceded by  the  sign  -f ; negative  terms  by  the  sign  — . When  a 
term  has  no  sign  before  it,  it  is  considered  positive. 

Like  terms  are  terms  which  contain  the  same  letters  affected 
with  the  same  exponents.  Thus:  7a^x^  and  — ba^x^  are  like 
terms.  When  positive  and  negative  like  terms  are  combined, 
the  result  is  called  their  algebraic  sum. 

Thus:  2a^x^  is  the  algebraic  sum  of  7a^x^  and  —ba'^x^. 

Equal  terms  are  like  terms  that  have  the  same  numerical 
coefficient.  Thus:  7a'^x^  and  —7a}x^  are  equal  terms  with 
unlike  signs.  When  positive  and  negative  equal  terms  occur 
in  the  same  expression,  they  neutralize  each  other,  or  cancel. 

The  numerical  value  of  an  algebraic  expression  is  the  result 
obtained  by  assigning  a numerical  value  to  each  letter  and 
performing  the  operations  indicated.  Thus,  the  numerical 
value  of 

4a-\-3bc  — d^, 

when  a = l,  6 = 2,  c = 3,  and  d = 4,  is 
4X1+3X2X3-4X4  = 4+18-16  = 6. 


52 


GUNNERY 


PROBLEMS. 

Find  the  numerical  value  of  the  following  expressions, 
when  a = l,  6 = 2,  c = 3,  and  d = 4. 


1. 

2. 

3. 


3a2&2  — 2(a+d+l).  Ans.  0. 

— ^ ^X(a+d).  Ans.  10. 

ab^  — c — a^  4a^  — 6+(f 
5 ^ ~33  • 


Of  the  following. 


when  a = 4,  6 = 3,  c = 2,  and  d=l: 

. a 6 , , 

4.  — — — +c  — d.  Ans.  2. 


5. 


Ans.  15. 


6.  3[(a26+l)d]=-(a26+d).  Ans.  3. 


Of  the  following, 

when  «;  = 1,435,  p = 13.08,  d = 8,  w = 290; 


also,  when  y=  1,335,  p=  16.25,  d=12,  w = 800: 

7.  — 608.3]p+0.14d)  I . Ans.  approximately  0 and  .8. 

In  dealing  with  the  more  simple  algebraic  expressions,  the 
following  rules  apply: 


Addition. 

Case  I. — When  the  quantities  to  be  added  are  like 

TERMS. 

Rule. — Add  the  coefficients  of  the  positive  and  negative  terms 
separately;  subtract  the  less  sum  from  the  greater,  prefixing  the 
sign  of  the  greater;  to  the  result  annex  the  common  literal  part. 


ALGEBRAIC  EXPRESSIONS  AND  SIMPLE  EQUATIONS  53 


Case  II. — When  all  the  quantities  to  be  added  are  not 

LIKE  TERMS. 

Rule. — Write  the  quantities  to  be  added  so  that  like  terms 
shall  fall  in  the  same  column;  add  each  column  separately,  annex- 
ing unlike  terms  with  their  proper  signs. 

PROBLEM. 

Add  3a^  — 2&2— 4a6,  Sa^  — b^+2a6,  and  3ab—3c‘^  — 2b\ 

Solution:  3a^ — 4^ab  — 2b^ 

5a^-{-2ab  — b^ 

+3ab-2b^-3c^. 

Algebraic  sum,  8a^  -\-ab  — h¥  — 3c^,  Ans. 
Subtraction. 

Rule. — Change  the  sign  of  each  term  of  the  subtrahend,  or 
conceive  it  to  be  changed,  and  then  proceed  as  in  addition. 

When  positive  and  negative  terms  are  thus  subtracted,  the 
result  is  called  their  algebraic  difference. 

problem. 

From  4a^6a:+acx+3a62-f  c2  subtract  a%x-acx-{-‘iab^  — d. 

Solution:  Minuend,  4:a%x-\-acx-\-3ab^-\-c 

Subtrahend,  a^bx  — acx + 4a&^  — d 

Algebraic  difference,  3a^bx-\-2acx  — ab^-\-c-\-d,  Ans. 

Use  of  the  parentheses. — When  the  sign  + is  before  parenthe- 
ses, the  parentheses  may  be  omitted.  Thus:  a-f-(6-bc  — d)  = 
a-j-b-\-c  — d. 

When  the  sign  — is  before  parentheses,  the  parentheses 
may  be  omitted,  if  the  sign  of  every  term  within  the  parentheses 
be  changed.  Thus:  a — Q)  — c)=a  — b-\-c;  Ga^— (3a6-f2c^)  = 
Qa^  — 3ab'~2c^. 


54 


GUNNERY 


Any  number  of  successive  parentheses  or  brackets  may  be 
removed  by  these  rules  by  omitting  first  the  innermost  'paren- 
theses, then  the  next  innermost,  and  so  on. 

Conversely,  any  number  of  terms  of  an  expression  may  be 
put  in  parentheses,  and  the  sign  + placed  before  the  whole; 
or  the  sign  — may  be  placed  before  the  whole,  provided  the 
sign  of  every  term  included  in  the  parentheses  he  changed. 

Multiplication. 

To  MULTIPLY  ONE  TERM  BY  ANOTHER. 

Rule. — Multiply  the  coefficients  together  for  a new  coefficient; 
after  this  product,  write  all  the  letters  in  both  terms,  giving  to  each 
letter  an  exponent  equal  to  the  sum  of  its  exponents  in  the  two 
terms,  or  factors. 

If  the  terms  have  like  signs,  the  sign  of  the  product  will  be 
+ ; if  unlike,  it  will  be  — . Thus:  ahxXah^x  = a^¥x^;  —abxX 
2a%x^  = — 2a%^x^ ; ( — ax)X{  — 2acx)  = 2a^cx^. 

In  finding  the  continued  product  of  several  terms,  if  the 
number  of  negative  terms  is  even,  the  product  will  be  positive; 
if  odd,  the  product  will  be  negative. 

When  one  of  the  factors  is  composed  of  more  than  one 
term,  each  term  must  be  multiplied  by  the  other  factor,  and 
the  results  connected  by  their  proper  signs.  Thus:  (acx  — a%x 
+ 2a:)  X ( — 3a)  = — Sa^cx + 3a%x  — Qax. 

Division. 

To  DIVIDE  ONE  TERM  BY  ANOTHER. 

Rule. — Divide  the  coefficient  of  the  dividend  by  that  of  the 
divisor  for  a new  coefficient;  after  the  new  coefficient  write  all 
the  letters  of  the  dividend,  giving  to  each  letter  an  exponent  equal 
to  its  exponent  in  the  dividend  minus  that  in  the  divisor. 

If  the  dividend  and  divisor  have  like  signs,  the  quotient 
will  be  positive;  if  unlike,  it  will  be  negative.  Thus:  4a%x--i-2ab 
= 2ax;  Qa^bx-^{  — Sax)  = —2ab;  (— 4ab) 4- ( — 2&)  =2a. 


ALGEBRAIC  EXPRESSIONS  AND  SIMPLE  EQUATIONS  55 


If  the  dividend  contain  several  terms,  and  the  divisor  but 
one,  each  term  of  the  dividend  must  be  divided  as  above,  and 
the  results  connected  by  their  proper  signs.  Thus:  (Qa^  — 2ahx 
+9aa:)  -i-3a  = 2a  — ^hx-{-dx. 

In  the  division  of  single  terms,  when  the  coefficient  of  the 
quotient  is  a whole  number  and  the  exponents  of  all  the  letters 
that  enter  it  are  'positive,  the  division  is  exact. 

In  all  other  cases  the  quotient  is  essentially  fractional,  and 
the  division  is  inexact.  In  such  cases,  all  factors  common  to 
both  dividend  and  divisor  should  be  canceled,  and  the  division 
of  the  other  factors  indicated.  Thus: 

12a*6®c^  3aX4a’6®c'^  3a  „ 

= = — = ^ac~^ ' 

Wh^c^  4c^X4:aW  4c^  ’ 

in  which  the  exponent  of  b has  been  reduced  to  zero,  and  that 
of  c is  negative. 

Zero  power  and  negative  exponents. — Let  the  powers  of  any 
positive  quantity  represented  by  a be  arranged  in  a decreasing 
order.  Thus:  a^,  a*,  a^,  a^,  ah 

From  this  it  is  evident  that  the  subtraction  of  1 from  the 
exponent  of  any  quantity  is  equivalent  to  dividing  the  quantity 
by  itself. 

If  the  subtraction  be  continued,  the  result  will  be  a®,  ah  ah 
ah  ah  a°,  a~h  a~h  a~h  and  so  on. 

Then,  from  the  principle  just  stated,  a°  = a^-7-a—-=l; 

a 

a-l  = a“-^a  = l-^•a  = -;  a-2  = a-^^a  = --i- a =-2;  a-^  = a-^A-a  = 
a a a 

-2-:-a  = -3;  and  so  on. 
a a 

Whence  it  appears  that  any  quantity  with  a zero  exponent, 
or  raised  to  the  zero  power,  is  equal  to  1;  and  that  any  quantity 
with  a negative  exponent  is  equal  to  1 divided  by  the  quantity 
with  an  equal  positive  exponent. 


56 


GUNNERY 


1 divided  by  a quantity  is  called  the  reciprocal  of  the 
quantity. 

Simple  Equations. 

An  equation  is  a statement  of  the  equality  of  two  expressions. 
It  is  composed  of  two  parts  called  members,  connected  by  the 
sign  of  equality;  the  part  on  the  left  of  the  sign  is  called  the  1 st 
member,  that  on  the  right  the  2d  member.  Thus;  x-\-a  = b—c 
is  an  equation;  x-\-a  is  the  1st  member,  b — c the  2d  member. 

Equations  containing  but  one  unknown  quantity  are  divided 
into  different  degrees,  or  orders,  according  to  the  highest  power 
of  the  unknown  quantity  found  in  any  term.  Thus: 

2a;  — 3 = 9,  is  an  equation  of  the  1st  degree. 

2x^  — Sx  — 9 is  an  equation  of  the  2d  degree. 

A simple  equation  is  an  equation  of  the  1st  degree. 

The  root  of  a simple  equation  is  the  value  which  will  make 
its  members  equal  when  substituted  for  the  unknown  quantity. 
Thus:  6 is  the  root  of  2a:  — 3 = 9. 

To  solve  a simple  equation  is  to  find  its  root.  The  opera- 
tions required  in  solving  equations  depend  upon  the  following 
general  principles: 

1.  Both  members  of  an  equation  may  be  increased  or  dimin- 
ished by  the  same  quantity  without  destroying  the  equality. 

2.  Both  members  of  an  equation  may  be  multiplied  or 
divided  by  the  same  quantity  without  destroying  the  equality. 

These  principles  are  derived  from  the  self-evident  truth 
that — 

If  the  same  operation  be  performed  upon  equal  quantities 
the  results  will  be  equal. 

The  two  principal  operations  employed  in  sohfing  simple 
equations  are  transposing  and  clearing  of  fractions. 

Transposing  is  changing  a term  from  one  member  to  the 
other.  Any  term  may  be  transposed  if  its  sign  be  changed.  For, 
in  this  operation,  the  same  quantity  is  added  to  or  subtracted 
from  each  member  of  the  equation. 


ALGEBRAIC  EXPRESSIONS  AND  SIMPLE  EQUATIONS  57 


The  signs  of  all  the  terms  of  each  member  may  be  changed, 
for  this  is  in  effect  multiplying  each  term  of  both  members  by 
the  same  quantity,  — !. 

Clearing  of  fractions  is  reducing  the  terms  of  a simple 
equation  to  a common  denonoinator  and  then  multiplying 
every  term  by  this  denominator,  or,  what  amounts  to  the  same 
thing,  omitting  the  denominator. 

To  CLEAR  AN  EQUATION  OF  FRACTIONS. — Multiply  each 
numerator  hy  the  denominators  of  all  the  other  fractions,  and  omit 
the  denominators. 

If  any  fraction  whose  numerator  consists  of  more  than  one 
term  is  preceded  by  a minus  sign,  care  must  be  taken  to  change 
the  sign  of  every  term  of  the  numerator  when  the  denominator 
is  omitted.  Mistakes  may  often  be  avoided  by  inclosing 
the  numerator  in  parentheses  before  omitting  the  denominator; 
then,  after  omitting  denominator,  changing  the  sign  of  every 
term  in  the  parentheses  and  omitting  the  latter. 

To  SOLVE  A SIMPLE  EQUATION. 

Rule. — Clear  the  equation  of  fractions  and  perform  all  oper- 
ations indicated;  transpose  all  terms  containing  the  unknown 
quantity  to  the  first  member,  all  others  to  the  second,  and  combine 
like  terms;  separate  the  first  member  into  two  factors,  one  of  which 
shall  be  the  unknown  quantity,  the  other  the  algebraic  sum  of  its 
coefficients;  divide  both  members  by  the  coefficient  of  the  unknown 
quantity;  the  second  member  of  the  resulting  equation  will  be  the 
required  root. 

The  result  may  be  verified  by  substituting  the  root  found 
in  the  given  equation.  If  it  makes  the  two  members  equal, 
the  result  is  correct. 


PROBLEMS. 


Solve  the  following  equations: 


a-\-bc 


1. 


u~}~  1 

x — c = x 

2 


58 


GUNNERY 


Clearing  of  fractions, 

h(a-\-l)x  — 2hc  — 2bx  — 2{a-\-bc); 

performing  multiplications  indicated  and  omitting  parentheses, 
abx  -\-bx  — 2bc  = 2bx  — 2a  — 26c 

transposing, 

abx-\-bx  — 2bx=  — 2a— 26c+26c; 
combining  like  terms, 

abx  — bx=—2a‘, 
factoring  the  first  member, 

{ab  — b)x=  — 2a; 


dividing  by  coefficient  of  x, 


— 2a  . 
x=-T — r,  Ans. 
ab  — b 


2.  x+18  = 3a:  — 5.  Ans.  x = ll|. 

6 3ti 

3.  Zax+-^  — ^ = bx  — a.  Ans.  x = 

X S X X 19  . ooi 

4.  — = 20 . Ans.  a:  = 23j. 

2 3 2 

rc+3  X ^ x — 5 ^ , 

5.  = ^ = 

4x  — 2 3a;  — 1 

6.  2x— — :^  = — ;r- . Ans.  rc  = 3. 


7.  3a;- 


5 2 

bx  — d 


= x+a.  Ans.  a;  = 


Za  — d 
6^' 


ax-b  . a bx  bx-a^  36 


3 2 


3a— 26 


8. 


3 


PART  II 

GUNPOWDER  AND  HIGH  EXPLOSIVES 


Taken  from  Artillery  Circular  B,  1902 


'i 


) 


I 


( 


GUNPOWDER  AND  HIGH  EXPLOSIVES 


CHAPTER  I 

COMBUSTION,  EXPLOSION,  DETONATION 

Ordinary  Combustion. — In  all  explosions,  the  changes  that 
occur  may  be  considered  the  direct  results  of  ordinary  com- 
bustion, the  manifestations  of  which,  such  as  heat,  light, 
etc.,  are  universally  known. 

In  their  relation  to  combustion,  all  substances  may  be  clas- 
sified, first,  as  combustibles,  or  substances  which  burn,  e.  g., 
wood,  coal,  fats,  oils,  gas,  etc.;  and  incombustibles,  or  sub- 
stances which  do  not  burn,  e.  g.,  glass,  porcelain,  earthen- 
ware, granite,  etc.;  secondly,  as  supporters  of  combustion, 
or  those  substances  which  aid  or  sustain  combustion,  e.  g., 
air,  oxygen  (a  gas),  etc.;^  and  non-supporters  of  combustion,  or 
those  substances  which  retard  combustion,  e.  g.,  nitrogen  (a 
gas),  etc. 

In  order  that  combustion  may  occur,  or  a substance  burn, 
a combustible  and  a supporter  of  combustion  must  be  brought 
together,  and  the  temperature  of  the  combustible  raised  to 
a point  at  which  it  may  unite  with  the  supporter  of  combustion.  ^ 

The  temperature  at  which  a combustible  begins  to  burn 

* The  most  energetic  supporter  of  combustion  is  oxygen  (a  colorless,  odorless, 
transparent  gas).  Air,  the  most  common  supporter  of  ordinary  combustion,  is 
such  only  by  reason  of  the  oxygen  it  contains,  air  being  composed  of  23  parts  of 
oxygen  and  77  parts  of  nitrogen  (approximately). 

^ What  actually  occurs  is,  the  elements  of  which  the  combustible  is  composed 
unite  chemically  with  the  oxygen  of  the  supporter  of  combustion,  forming  new 
and  entirely  different  products.  This  disintegration  and  union  is  generally 
brought  about  by  the  action  of  heat. 


61 


62 


GUNNERY 


is  called  its  “point  of  ignition f’  and  this  point  varies  between 
very  wide  limits;  thus,  phosphorus  ignites  at  150°  F.,  sulphur 
at  480°  F.,  while  several  substances  require  a temperature 
over  1,000°  F.  for  their  ignition. 

Combustion  may  be  started,  or  a substance  ignited  in  various 
ways;  e.  g.,  by  contact  with  a heated  body  (such  as  a flame), 
by  friction,  percussion,  concussion,  an  electric  spark  or  cur- 
rent, etc. 

The  combustion  of  a substance  may  be  promoted  or  increased 
by  intimately  mixing  the  combustible  and  supporter  of  com- 
bustion. 

Thus,  in  order  to  kindle  a fire  rapidly,  the  wood  is  cut  into 
small  pieces  or  shavings.  In  the  same  way  sawdust,  if  the 
particles  be  separated  or  suspended  in  the  air  so  that  they 
may  be  surrounded  by  or  thoroughly  mixed  with  it,  burns 
far  more  energetically  or  intensely  than  the  wood  from  which 
it  was  obtained. 

The  principal  manifestations  of  combustion  are  heat,  light, 
and  gas,  the  first  two  being  always  perceptible  to  the  senses, 
the  latter  being  sometimes  visible  in  the  form  of  smoke,  and  at 
other  times  invisible. 

Of  these  accompanying  phenomena,  the  most  important, 
from  an  explosive  point  of  view,  is  the  last  mentioned,  gas, 
and  next  in  importance  is  the  heat  which  causes  the  gas  to 
expand. 

Recapitulation. — 1.  Combustion  is  an  example  of  chemical 
change,  in  which  the  combustible  unites  with  the  oxygen  of 
the  supporter  of  combustion. 

2.  In  ordinary  combustion  the  oxygen  is  supplied  by  the 
air. 

3.  The  most  energetic  supporter  of  combustion  is  pure 
oxygen. 

4.  To  ignite  a combustible,  or  cause  a substance  to  burn, 
its  temperature  must  be  raised  to  its  point  of  ignition,  and 
this  may  be  done  in  various  ways. 


COMBUSTION,  EXPLOSION,  DETONATION 


63 


5.  Combustion  may  be  promoted  or  increased  by  intimately 
mixing  the  combustible  and  supporter  of  combustion. 

6.  The  most  important  of  the  manifestations  of  ordinary 
combustion,  from  an  explosive  point  of  view,  are  gas  and  heat. 

Very  Rapid  Combustion,  or  Explosion. — Explosion  is  gener- 
ally defined  as  a chemical  change  which  results  in  the  very  rapid 
formation  of  a very  great  volume  of  highly  expanded  gas. 

As  has  already  been  stated,  gas  is  one  of  the  principal  prod- 
ucts of  combustion,  and  it  is  also  accompanied  by  heat, 
which  causes  the  gas  to  expand,  therefore  the  relation  existing 
between  combustion  and  explosion  should  be  very  close.  As 
a matter  of  fact,  such  is  the  case,  the  only  difference  between 
the  two  phenomena  being  the  length  of  time  required  to 
bring  about  the  change.  In  other  words,  combustion  is  only 
a slow  form  of  explosion,  or  explosion  a very  rapid  form  of 
combustion. 

An  explosive  may  be  defined  as  a substance  or  a mixture  of 
substances  which,  when  heated,  struck,  or  subjected  to  the  shock 
of  another  explosive,  may  result  in  the  extremely  rapid  formation 
of  a very  great  volume  of  highly  heated  gas. 

The  first  requisite,  then,  of  an  explosive  is  that  it  shall 
have  sufficient  oxygen  to  promote  and  sustain  very  rapid 
combustion.  This  supply  of  oxygen,  not  being  found  in  the 
air,  must  be  contained  in  the  combustible  elements  of  the 
explosive,  or  in  other  substances  which  are  added  for  the 
purpose. 

The  principal  substances  thus  used  are  potassium  nitrate 
(India  saltpeter,  or  niter),  sodium  nitrate  (Chile  or  cubical 
saltpeter),  potassium  chlorate,  nitric  acid,  etc.  In  these  sub- 
stances, which  are  called  “oxidizers,”  or  “oxidizing  agents,”  the 
oxygen  occurs  in  combination  with  other  elements,  and  is 
liberated  or  set  free  in  the  form  of  gas  by  the  action  of  external 
agents,  such  as  heat,  acids,  etc. 

A second  requisite  for  an  explosive  which  follows  directly 
from  the  definition  given  is  that  the  combustible  element 


64 


GUNNERY 


and  supporter  of  combustion  (in  this  case  the  “oxidizer”) 
shall  be  very  intimately  mixed  so  that  the  combustion  may 
occur  as  far  as  possible  in  an  atmosphere  of  oxygen.  The 
combustibles  previously  mentioned  (as  well  as  the  majority 
of  others  used  in  making  explosives^  contain  essentially  car- 
bon, hydrogen,  and  oxygen.  At  the  moment  of  explosion 
(or  combustion,  depending  upon  the  length  of  time  occupied 
during  the  change)  the  carbon  unites  with  a part  of  the  oxygen 
to  form  gases  called  carbonic  acid  and  carbonic  oxide;  the 
hydrogen  unites  with  another  part  to  form  water  in  the  form 
of  steam,  while  any  excess  of  oxygen  is  either  set  free  as  an 
elementary  gas  or  unites  with  other  elements  that  may  be 
present. 

While  these  gases  themselves  occupy  a much  greater  volume 
than  the  original  substance  or  substances  from  which  they 
are  obtained,  still  the  third  requisite  of  an  explosive  is  found 
in  the  heat  produced  during  the  explosion,  which  serves  to 
further  expand  these  gaseous  products. 

Recapitulation. — 1.  Explosion  is  only  a very  rapid  form  of 
combustion. 

2.  The  first  requisite  of  an  explosive  is  that  it  shall  contain 
sufficient  oxygen  to  promote  and  sustain  energetic  and  very 
rapid  combustion. 

3.  The  oxygen  may  be  contained  in  the  combustible  itself 
or  supplied  by  other  substances  added  for  that  purpose. 

4.  The  second  requisite  of  an  explosive  is  that  the  products 
of  explosion  shall  be  chiefly  gaseous. 

5.  These  gases  are  formed  by  the  union  of  the  elements 
of  the  combustibles  with  the  oxygen  of  the  oxidizers  added 
for  that  purpose,  as  well  as  to  intensify  the  combustion. 

6.  The  third  requisite  of  an  explosive  is  found  in  the  heat 
produced  during  the  explosion  which  serves  to  greatly  expand 
the  gases  produced  at  the  same  time. 

' Except  sulphur,  which  unites  with  oxygen  to  form  various  products,  solid 
and  gaseous. 


COMBUSTION,  EXPLOSION,  DETONATION 


65 


Instantaneous  Combustion  or  Detonation. — Detonation  may 
be  defined  as  the  instantaneous  combustion  of  the  entire  mass  of 
the  combustible,  and  is  therefore  only  an  extremely  rapid 
form  of  explosion. 

Practically  this  definition  is  incorrect,  since  even  in  detona- 
tion there  must  always  be  some  interval  of  time  in  order  that 
the  explosion  may  be  propagated  from  one  particle  of  the 
explosive  to  another.  The  rate  or  velocity  of  detonation  has 
been  determined  for  some  substances;  e.  g.,  that  for  dry  com- 
pressed guncotton  has  been  found  to  be  from  17,000  to  18,000 
feet  per  second,  or  about  200  miles  per  minute. 

From  the  relation  existing  between  combustion,  explosion, 
and  detonation,  the  first  requisite  of  a detonating  substance 
is  that  the  union  between  the  combustible  and  supporter  of 
combustion  shall  be  the  closest  possible. 

In  the  case  of  exploding  substances,  or  those  explosives  which 
under  normal  conditions  merely  explode,  the  combustible  and 
oxidizer  are  mixed  mechanically.  Thus,  in  gunpowder  the 
charcoal,  sulphur,  and  niter  are  separately  pulverized,  and 
then  mixed  as  thoroughly  as  possible  by  proper  machines. 

This  degree  of  incorporation,  or  mixing,  is  not  sufficiently 
intimate  in  the  case  of  detonating  substances,  and  in  order  to 
secure  the  closest  possible  union  of  the  necessary  elements, 
they  are  mixed  chemically.  Thus,  in  the  case  of  nitroglycerin, 
when  glycerin  is  poured  slowly  into  nitric  acid,  the  latter  acts 
upon  the  former  chemically,  and  forms  an  entirely  new  com- 
pound substance,  in  which  the  elements  are  in  the  closest 
possible  union. 

Explosive  Mixtures  and  Explosive  Compounds. — From  the 
different  manner  in  which  the  elements  of  explosive  substances 
are  united  results  the  most  important  division  in  the  classi- 
fication of  explosives,  viz.: 

Explosive  mixtures  are  those  explosive  substances  in  which 
the  elements  or  ingredients  are  mixed  mechanically,  and  may 
be  separated  by  mechanical  means. 


66 


GUNNERY 


Explosive  compounds  are  those  explosive  substances  in  which 
the  elements  or  ingredients  are  united  chemically,  and  can  be 
separated  only  by  chemical  means. 

From  what  has  just  preceded,  the  natural  deduction  is 
that  explosive  mixtures  “explode,”  while  explosive  compounds 
“detonate,”  and  such  may  be  considered  the  normal  action 
of  these  two  classes  of  explosives^ 

However,  under  certain  conditions,  their  relative  actions 
may  be  reversed,  while  explosives  of  both  classes,  if  ignited 
in  small  quantities  and  unconfined  generally,  burn  away 
harmlessly.  ^ 

Methods  Employed  to  Cause  Explosives  to  Explode. — As  in 

the  case  of  combustibles  the  point  of  ignition  varies  with 
each  substance,  so,  with  explosive  mixtures,  each  has  its 
“exploding  point, to  or  beyond  which  its  temperature  must 
be  raised  in  order  to  produce  explosion.  With  explosive  com- 
pounds, however,  detonation  can  with  certainty  be  produced 
only  by  an  initial  explosion  of  fulminate  of  mercury,  or  by 
that  of  a second  detonating  substance.  This  peculiarity  in 
the  action  of  explosive  compounds  is  explained  by  the  theory 
that  when  fulminate  of  mercury  is  exploded  it  sets  up  a 
vibratory  motion  to  which  detonating  substances  are  par- 
ticularly susceptible,  and  which  causes  their  instantaneous 
disintegration. 

The  more  usual  methods  practically  employed  to  cause 
explosives  to  explode  are: 

1.  Ignition,  as  when  gunpowder  is  fired  by  means  of  a 
wire  heated  by  the  passage  through  it  of  an  electric  current. 

2.  Inflammation,  as  when  gunpowder  is  fired  by  the  flame 
produced  by  the  ignition  of  a fuse. 

^According  to  their  mode  of  action,  explosives  are  sometimes  classified  as 
“low  ejiplosives,”  or  those  which  explode,  and  “high  explosives,”  or  those  which 
detonate. 

^As  used  in  smokeless  powders,  the  action  of  explosive  compounds  is  so  regu- 
lated as  to  eliminate  the  possibility  of  detonation.  This  result  in  the  case  of 
nitrocellulose  powders  is  accomphshed  by  the  process  of  “ coUoiding.” 


COMBUSTION,  EXPLOSION,  DETONATION 


67 


3.  Percussion,  as  in  the  firing  of  percussion  caps  and  metallic 
caps  and  metallic  cartridges  in  small  arms. 

4.  Friction,  as  seen  in  the  use  of  ordinary  friction  primer. 

5.  Detonation,  as  when  fulminate  of  mercury  is  used  in 
blasting  caps,  torpedo  detonators,  etc. 

Recapitulation. — 1.  In  detonation  the  time  required  to 
accomplish  the  change  is  reduced  to  a minimum,  and  the 
combustion  (or  explosion)  may  be  considered  practically 
instantaneous. 

2.  Detonating  substances  are  chemical  compounds,  in  which 
each  minutest  particle  contains  in  itself  all  the  necessary 
elements  for  its  combustion  (or  explosion). 

3.  Explosive  mixtures  are  those  explosive  substances  in 
which  the  elements  or  ingredients  are  mixed  mechanically. 

4.  Explosive  compounds  are  those  explosive  substances  in 
which  the  elements  or  ingredients  are  united  chemically. 

5.  Under  normal  conditions  explosive  mixtures  explode, 
while  explosive  compounds  detonate. 

6.  The  more  usual  methods  of  causing  explosion  are  igni- 
tion, inflammation,  percussion,  friction  and  detonation. 


CHAPTER  II 


EXPLOSIVE  MIXTURES— GUNPOWDER 

Gunpowder.  1 — Gunpowder  may  be  taken  as  a representative 
explosive  mixture.  It  is  a very  intimate  mixture  of  potassium 
nitrate  (saltpeter  or  niter),  sulphur,  and  charcoal.  Although 
these  substances  do  not  act  upon  each  other  at  the  ordinary 
temperature,  when  thoroughly  mixed  and  heated  they  are 
momentarily  dissociated  (separated) , the  elements  immediately 
rearranging  themselves  as  new  products  which  are  largely  in 
the  form  of  highly  heated  gas. 

Ingredients  of  Gunpowder. — The  ingredients  of  gunpowder 
are  easily  obtained  and  in  large  quantities,  saltpeter  and  sul- 
phur occurring  naturally,  the  one  mixed  in  the  soil  of  certain 
countries,  notably  India,  the  other  in  caves  and  the  \dcinity  of 
volcanoes,  while  charcoal  is  merely  the  residue  of  charred 
wood. 

Proportions  of  the  Ingredients. — The  three  ingredients  of 
gunpowder  may  be  mixed  in  greatly  varying  proportions  and 
each  mixture  will  be  explosive,  but,  for  ordinary  service  gun- 
powder, experience  has  shown  that  a powder  containing — 

Saltpeter  75  parts 

Sulphur 10  parts 

Charcoal  15  parts 

is  the  best,  and  until  recently  the  majority  of  military  nations 
adopted  it. 

The  large  proportion  of  sulphur  used  in  the  earlier  powders 

^ Gunpowder  and  its  manufacture  are  described  because  certain  of  these 
powders  are  still  retained  in  the  service. 

68 


EXPLOSIVE  MIXTURES— GUNPOWDER 


69 


is  no  longer  necessary  since  the  introduction  ^ of  percussion 
caps,  friction  primers,  etc,;  and  since  when  present  in  large 
quantities  it  introduces  in  the  powder  certain  disadvantages, 
the  percentage  of  sulphur  in  modern  gunpowders  is  reduced 
as  much  as  possible,  being  only  from  2 to  3 per  cent,  in  the 
cocoa  powders,  which  are  decidedly  the  best  for  guns  of  large 
caliber. 

In  order  to  secure  uniform  results  and  safety  during  the 
process  of  manufacture,  the  ingredients,  before  being  mixed, 
are  separately  pulverized.  The  saltpeter,  if  used  immediately 
after  being  purified,  is  sufficiently  fine  and  requires  no  further 
reduction;  but  if  it  has  been  stored  and  become  caked,  it,  like 
the  sulphur,  is  ground  to  a very  fine  powder  in  a machine 
similar  to  an  ordinary  “mortar-mill.”  Because  it  is  very 
porous  and  quickly  absorbs  moisture,  the  charcoal  is  not  stored 
in  large  quantities  or  for  any  length  of  time,  but  is  prepared 
about  two  weeks  before  it  is  required  for  use,  when  it  is  ground 
to  powder  in  a machine  resembhng  a large  “coffee-mill,” 
and  then  stored  in  air-tight  metal  boxes. 

Manufacture  of  Gunpowder. — The  ingredients  are  now 
ready  for  the  manufacture  of  the  powder,  which  consists  of 
the  following  processes: 

1.  Mixing  the  ingredients.— A.  50-pound  charge  is  carefully 
weighed  in  the  proper  proportions  and  placed  in  a gun-metal 
or  copper  barrel  (or  drum),  through  the  center  of  which 
passes  an  axle  to  which  are  attached  several  fork-shaped  arms, 
also  made  of  gun  metal.  When  in  operation  the  barrel  and 
axle  carr^dng  the  arms  revolve  in  opposite  directions,  and 
at  the  end  of  five  minutes  the  charge  is  thoroughly  mixed. 

2.  Incorporating  or  “milling.” — Thecharge  is  next  uniformly 
spread  in  the  “incorporating  rr>ill”  and  slightly  moistened  with 

^ In  gunpowder,  saltpeter  acts  as  the  oxidizer  and  charcoal  as  the  combustible, 
while  the  sulphm-  was  originally  added  to  lower  the  point  of  ignition,  although 
it  also  served  to  increase  the  amount  of  heat  produced  and  to  further  expand  the 
gases. 


70 


GUNNERY 


water/  and  subjected  to  continued  grinding  under  heavy 
rollers.  The  product  is  known  as  “mill-cake.” 

3.  Breaking  down  the  “mill-cake.” — After  removal  from  the 
incorporating  mill,  the  mill-cake  is  “broken  down,”  or  reduced 
to  “powder  meal,”  by  being  passed  through  two  pairs  of  gun- 
metal  toothed  rollers. 

4.  Pressing. — The  powder  meal  is  next  placed  in  the  “press 
box,”  where  it  is  compressed  into  hard  slabs  or  sheets.  Next 
to  incorporation,  pressing  is  the  most  important  step  in  making 
gunpowder.  The  principal  advantages  obtained  by  pressing 
are : first,  the  slabs  or  sheets  when  made  into  grains  of  the  re- 
quired size  absorb  less  moisture  from  the  air;  second,  the  last- 
ing qualities  of  the  powder  are  greatly  increased;  third,  the 
powder  is  less  liable  to  be  reduced  to  powder  in  transportation ; 
and,  finally,  it  supplements  the  object  sought  in  incorporating, 
inasmuch  as  by  it  the  ingredients  are  brought  into  a closer 
union,  thereby  producing  greater  uniformity  in  the  grain. 
The  effect  of  pressing  upon  the  density  of  the  powder  can  not 
be  overestimated  and  will  be  referred  to  again. 

5.  Granulating. — The  slabs  or  sheets  as  they  come  from  the 
press  box  are  known  as  press  cake,  and  are  passed  to  the  gran- 
ulating machine,  which  is  similar  to  the  breaking-down  ma- 
chine, consisting  essentially  of  three  or  four  pairs  of  gun- 
metal  toothed  rollers,  the  size  of  the  teeth  of  which  vary 
according  to  the  size  of  grain  required. 

6.  Dusting.— The  granulated  powder  is  next  passed  through 
revolving  reels  covered  with  canvas  cloth  in  which  the  dust 
formed  during  the  last  step  is  removed. 

7.  Glazing. — As  a general  rule,  all  modern  mihtary  powders 
are  glazed.  This  is  done  by  introducing  the  charge  of  granu- 
lated powder  in  oaken  barrels  containing  small  quantities  of 
graphite  or  plumbago  (about  one-half  ounce  of  graphite  to 

^ This  is  done  for  the  threefold  purpose  of  preventing  powder-dust  from  flying 
about,  facilitating  the  incorporation,  and  reducing  the  effects  of  an  explosion  in 
case  of  an  accident. 


EXPLOSIVE  MIXTURES— GUNPOWDER 


71 


one  hundred  pounds  of  powder),  and  causing  the  barrels  to 
revolve  rapidly.  At  the  end  of  six  hours  the  grains  will  have 
acquired  a fine  gloss,  while  all  sharp  angles  and  corners  will 
have  been  rounded  off. 

The  object  of  glazing  is  to  diminish  the  formation  of  dust 
during  transportation  and  to  render  the  powder  less  hygro- 
scopic (that  is,  less  liable  to  absorb  moisture  from  the  air). 

Properties  of  Gunpowder. — Good  gunpowder  should  be 
composed  of  hard  angular  grains  which  do  not  soil  the  fingers 
' when  handled,  and  have  a perfectly  uniform  dark-gray  color. 
The  grains  when  broken  should  present  a clean  fracture, 
homogeneous  in  appearance,  without  any  visible  specks  of 
saltpeter  or  sulphur,  and  of  a dark  grajdsh  or  brownish  color, 
according  to  the  kind  of  charcoal  used.  When  new  it  should 
be  free  from  dust,  and  a small  quantity  flashed  upon  a porce- 
lain or  copper  plate  should  leave  no  residue  or  foulness.  It 
should  not  absorb  more  than  from  0.5  to  1.5  per  cent,  of  water 
when  exposed  to  air  of  average  dryness.  The  grains  should  be 
suflficiently  hard  to  stand  transportation  without  being  broken. 

The  property  which  exercises  the  greatest  influence  upon 
the  general  character  and  action  of  gunpowder  is  its  density,^ 
which  should  vary  between  the  limits  of  1.60  and  1.85  accord- 
ing to  the  kind  of  powder. 

Density  must  not  be  confounded  with  hardness,  which  seems 
to  bear  a direct  relation  to  the  pressure  exerted  in  compres- 
sion (“pressing”).  Although  a very  high  density  can  not  be 
obtained  without  producing  a considerable  degree  of  hardness, 
still  a powder  may  be  very  hard  without  being  very  dense: 
For  example,  “powder  meal”  containing  6 per  cent,  of  water 
can  be  made  very  dense  by  the  apphcation  of  a moderate 
pressm-e,  while  that  containing  1 per  cent,  of  water  can  be 
brought  to  the  same  degree  of  density  only  by  the  exertion 

^ Density  is  the  ratio  which  the  weight  of  a given  volume  of  the  substance  (in 
this  case,  powder)  bears  to  the  weight  of  an  equal  volume  of  distilled  water  at 
60°  F. 


72 


GUNNERY 


of  enormous  force.  Of  the  resulting  powders  the  latter  will 
be  the  harder. 

No  experimental  proof  is  necessary  to  show  that  if  two  grains 
of  powder  of  equal  size,  one  of  which  is  twice  as  dense  as  the 
other,  be  ignited  in  the  open  air  the  denser  will  take  longer 
to  burn  completely;  for  the  former  not  only  has  a closer  and 
less  porous  texture  of  grain,  but  contains,  bulk  for  bulk,  a 
larger  amount  of  matter  to  be  burned  from  the  same  surface. 

It  is  evident,  therefore,  that  the  density  of  the  powder, 
which  can  be  varied  at  will,  must  be  its  most  important  -physi- 
cal quality,  or  property. 

Recapitulation. — Gunpowder  may  be  taken  as  the  repre- 
sentative of  the  explosive  mixtures,  and  consists  of  saltpeter 
(niter),  sulphur,  and  charcoal. 

The  several  steps  in  the  manufacture  of  gunpowder  and 
their  objects  are: 

(1)  Mixing  the  ingredients. 

(2)  Incorporating  the  ingredients,  to  bring  the  pulverized 

ingredients  into  such  intimate  contact  that  each 
particle  of  the  powder  shall  contain,  if  possible, 
a particle  of  each  ingredient. 

(3)  Breaking  down  the  “mill-cake,”  so  that  it  can  be 

introduced  into  the  press  box. 

(4)  Pressing,  to  give  strength  and  density  ‘ to  the  powder. 

(5)  Granulating,  to  regulate  the  surface  of  combustion. 

(6)  Dusting,  to  prevent  the  absorption  of  moisture,  and 

to  insure  uniformity  of  combustion. 

(7)  Glazing,  to  diminish  the  formation  of  dust  during 

transportation,  and  also  to  protect  the  grains 
from  the  action  of  the  moisture  of  the  air. 

Of  the  properties  of  gunpowder  enumerated,  the  most 
important  are  its  density  and  that  of  being  able  to  resist  the 
action  of  the  moisture  of  the  air. 

^ The  density  is  also  affected  by  the  kind  of  charcoal  used  and  the  amount  of 
water  used  to  moisten  the  ingredients  before  being  introduced  into  the  press  box. 


CHAPTER  III 


GUNPOWDER— Continued 

The  processes  described  in  the  preceding  chapter  refer  par- 
ticularly to  the  manufacture  of  powders  the  sizes  of  the  grains 
of  which  do  not  exceed  in  diameter  % inch.  When  a charge 
of  such  powder  is  burned  in  the  bore  of  a gun  the  flame  rushes 
rapidly  through  the  spaces  between  the  grains,  causing  very 
rapid  combustion  and  correspondingly  rapid  formation  of 
gas. 

With  ordinary  cannon  powder  it  has  been  found  that  seven- 
eighths  of  the  entire  charge  is  consumed  before  the  shot  passes 
over  one-third  the  length  of  the  bore ; this  action  of  the  powder 
causes  excessive  pressures  at  or  near  the  base  of  the  bore  of 
the  gun,  due  to  the  fact  that  the  evolution  of  gas  is  greatest 
while  the  velocity  of  the  projectile  is  least. 

Special  Powders. — Experiment  has  shown,  however,  that 
the  amount  of  gas  evolved  at  the  first  instant  of  inflamma- 
tion and  the  combustion  of  the  charge  can  be  measurably 
controlled  by  the  size  and  form  of  the  grain  and  the  density 
of  the  powder.  The  first  two  conditions  regulate  the  area  of 
surface  exposed  to  combustion,  while  by  increasing  the  den- 
sity of  the  powder  greater  resistance  is  offered  to  the  pene- 
tration of  the  hot  gases  through  the  grains,  and  the  rapidity 
of  burning  is  thereby  controlled. 

These  principles  are  now  so  universally  recognized  that 
special  powders  differing  in  these  features  are  manufactured 
for  use  in  guns  of  different  calibers  in  order  to  secure  the  best 
results.  Such  powders  are  called  special  powders.  The  forms 
of  grain  adopted  for  such  powders  are  regular  geometrical 

73 


74 


GUNNERY 


Fig.  1. 


figures,  such  as  hexagons,  cubes,  and  'prisms,  the  resulting 
powders  being  known  as  hexagonal,  cubical  (or  pebble  in 
England,  where  this  form  is  used),  and  prismatic. 

Hexagonal  Powder. — This  powder  is  still  retained  in 
the  United  States  Army  for  use  in  certain  old 
guns.  Each  grain  is  formed  of  two  truncated 
six-sided  pyramids,  which  are  united  base  to 
base,  the  plane  of  union  being  therefore  a hexa- 
gon. (See  Fig.  1.)  The  uniform  size  and  shape 
of  the  grain  insure  uniformity  in  position  and 
size  of  the  interstices  in  the  cartridge;  this  insures  uniformity 
in  density  of  loadings  which,  with  uniform  density  of  the 
grains,  produces  uniform  and  low  pressure,  and  uniform  and 
high  velocities. 

Manufacture  of  Hexagonal  Powder. — The  ingredients  them- 
selves, the  proportions  of  the  ingredients,  and  the  processes 
of  manufacture  of  hexagonal  powder  are  similar  in  every 
respect  to  those  already  described  up  to  the  completion  of 
the  “mill-cake.”  The  following  modifications  are  peculiar 
to  this  powder: 

Mealing. — The  "mill-cake,”  broken  with  wooden  or  copper 
mallets,  is  revolved  in  a cylinder  of  wire-woven  cloth  with 


wooden  balls  until  it  is  mealed. 

Pressing. — The  mealed  powder  is  then  moistened  and  care- 
fully pressed  between  metallic  plates  containing  dies  which 
correspond  to  the  truncated  six-sided  pyramids  already 
described.  The  powder  comes  from  this  machine  in  poly- 
hedral grains  connected  along  their  hexagonal  edges. 

Granulating. — The  press  cake  is  passed  through  rollers 
armed  with  teeth  set  at  an  angle  of  120  degrees  to  the  axis 
which  separate  the  grains. 

Glazing. — The  powder  is  next  glazed  by  being  run  into  a 
glazing  barrel  containing  highly  glazed  small-grained  powder 
(rifle  or  mortar). 

Brushing. — The  powder  is  next  passed  repeatedly  through 


GUNPOWDER 


75 


the  brushing  machine.  This  consists  of  a frame  with  brushes 
revolving  near  an  inclined  plane,  along  which  the  powder  is 
made  to  pass  by  the  motion  of  the  brushes. 

Drying. — The  powder  is  next  dried,  and  then  carefully 
examined;  its  density  and  granulation  determined,  a differ- 
ence of  two  grains  (or  granules)  to  the  pound  being  enough 
to  condemn  the  powder. 

Rebrushing,  Redrying,  and  Packing. — If  the  results  of  the 
preceding  examination  are  satisfactory,  the  powder  is  again 
passed  through  the  brushing  machine,  redried,  brushed  a 
third  time,  and  then  packed  in  barrels. 

Prismatic  Powders. — In  selecting  the  original  shape  for 
special  powders,  several  practical  considerations  led  to  the 
adoption  of  regular  geometrical  figures,  one  of  the 
first  experimented  with  being  the  right  hexagonal 
prism.  The  earlier  prismatic  powders  contained 
seven  perforations  (see  Fig.  2)  in  the  direction 
of  the  axis  of  the  prism,  one  in  the  center,  and 
one  within  each  angle.  It  was  soon  discovered,  however, 
that  it  was  impossible  to  make  the  walls  of  the  prisms  suffi- 
ciently strong  to  resist  the  action  of  the  heated  gases  rushing 
through  the  perforations,  the  result  being  that  the  prisms 
were  broken  up  and  reduced  practically  to  fine-grain  powder. 

A single  perforation  was  therefore  substituted,  and  as  thus 
modified  the  perforated  prismatic  powders  were 
used  by  the  majority  of  military  nations  of  the 
world  in  all  guns  of  large  caliber.  The  best-known 
prismatic  powder  is  the  brown  or  cocoa  powder. 
(See  Fig.  3.)  The  characteristic  color  (brown) 
of  this  powder  is  derived  from  the  charcoal  used,  which  is 
slightly  carbonized  or  charred  rye  straw,  while  the  propor- 
tions of  the  ingredients  are  as  follows: 


Saltpeter 80  parts. 

Sulphur 2 to  3 parts. 

Charcoal 18  to  17  parts. 


Fig.  3. 


Fig.  2. 


76 


GUNNERY 


The  theory  of  this  powder  is  that  ignition  occurs  first  in 
the  interior  of  the  grains  (i.  e.,  along  the  central  perforation), 
and  the  combustion  proceeds  uniformly  outward  until  the 
entire  prism  is  consumed.  By  this  action  of  the  powder, 
which  is  rendered  possible  by  the  shape  of  the  grain  and  the 
high  and  uniform  density  of  the  powder  (1.86),  the  smallest 
surface  of  combustion  is  exposed  to  inflammation  at  the  instant 
of  ignition,  when  the  velocity  of  the  projectile  is  least,  and 
constantly  increases  as  the  projectile  moves  down  the  bore 
and  acquires  its  greatest  velocity.  The  result  is  moderate 
and  uniformly  sustained  pressures  on  the  gun,  with  uniform 
and  high  initial  velocities.^ 

Recapitulation. — 1.  Small-grain  powders  burn  too  rapidly 
and  irregularly  to  be  used  in  guns  of  large  caliber. 

2.  Special  powders  burn  more  slowly  and  uniformly,  so 
that  excessive  pressures  on  the  gun  are  avoided,  and  more 
uniform  and  higher  velocities  are  imparted  to  the  projectile. 

3.  The  perforated  prismatic  powders  are  the  best  special 
powders. 

4.  The  granulation  of  prismatic  powders  is  uniform,  and 
the  rate  of  their  combustion  is  regulated  by  varying  the 
composition. 

^The  sizes  of  the  grains  of  brown  powder  are  practically  uniform,  being  of 
the  same  dimensions  for  8,  10,  and  12-inch  rifles.  The  rate  of  combustion  of 
these  powders  is  regulated  by  varying  their  composition,  the_r^  decreasing  as 
the  caliber  of  the  piece  increases. 


CHAPTER  IV 


SMOKELESS  POWDERS 

Although  black  and  brown  powders  are  still  used  to  a very 
limited  extent,  all  military  powers  have,  within  the  last 
twenty  years,  adopted  smokeless  powder  for  use  in  guns  of 
all  calibers.  Smokeless  powders  differ  radically  from  ordinary 
gunpowders,  both  in  composition  and  granulation.  Although 
various  substances  have  been  experimented  with,  all  military 
smokeless  powders  may  be  divided  into  two  classes: 

1.  Those  consisting  of  guncotton  alone. 

2.  Those  consisting  of  guncotton  and  nitroglycerin. 

In  the  United  States  powders  of  the  second  class  are  used 
in  small  arms,  rapid-fire,  field,  and  siege  guns,  while  those  of 
the  first  class  are  used  in  all  other  guns. 

Manufacture  of  Smokeless  Powder. — The  wet  guncotton 
as  it  comes  from  the  pulping  machine  is  transferred  to  an  appa- 
ratus called  “dehydrator,”  which  consists  of  a steel  cylinder, 
one  end  of  which  is  fitted  with  a perforated  plate.  A heavy 
solid-headed  piston  works  longitudinally  in  the  cylinder.  The 
first  action  of  the  piston  is  to  express  the  water  contained 
in  the  guncotton.  Alcohol  is  then  poured  into  the  dedydra- 
tor  and  forced  through  the  guncotton  until  the  alcohol  runs 
from  the  dehydrator  of  the  same  strength  as  when  introduced. 
Sufficient  alcohol  is  allowed  to  remain  in  the  guncotton  to 
act  as  a solvent.  The  guncotton  is  removed  from  the  dehy- 
drator in  the  form  of  a moist  cake,  is  broken  up,  put  into 
the  “mixer,”  and  the  requisite  amount  of  ether  added  to  thor- 
oughly dissolve  the  guncotton.  In  powders  of  the  second 
class  acetone  is  used  as  the  solvent  instead  of  alcohol  and 

77 


78 


GUNNERY 


ether,  and  the  nitroglycerin  is  dissolved  in  a part  of  the  acetone 
before  it  is  added  so  as  to  reduce  its  sensitiveness. 

The  ingredients  and  solvent  having  been  placed  in  the 
“mixer,”  the  workmen  withdraw  from  the  building,  and  the 
process  of  incorporation  is  begun.  It  requires  from  one  to 
two  hours  to  effect  thorough  incorporation,  at  the  end  of 
which  time  the  powder  appears  as  a pasty  mass.  The  powder 
is  next  compressed  into  a solid  cake  preparatory  to  passing 
through  the  graining  press.  Until  recently  the  paste  was 
rolled  into  sheets  of  varying  thickness  by  passing  it  between 
steam-heated  rollers,  and  the  fin- 
ished powder  is  still  frequently 
seen  in  this  form. 

The  sheets  of  powder  are 
placed  in  a drying  house,  where 
the  bulk  of  the  remaining  sol- 
vent is  driven  off,  when  they  are 
again  rolled  to  eliminate  the 
“blisters”  formed  by  the  escape 
of  the  solvent  from  the  interior 
of  the  sheets,  as  well  as  to  perfect  the  in- 
corporation. 

In  case  of  the  flake,  sheet,”  or  “strip” 
powders,  as  the  powder  comes  from  the  roll- 
ing machine,  it  is  of  the  consistency  of  india- 
rubber  and  the  thinner  sheets  or  strips  are  perfectlj^  translucent. 

Recently  the  perforated  cylindrical  grain,  either  single  or 
multiperf orated  (see  Figs.  4 and  5),  has  almost  entirely  super- 
seded the  earlier  forms  of  flake  and  strip  powder. 

In  making  the  cylindrical-grained  powders,  the  paste  is 
placed  in  a large  cjdinder  (made  of  cast  iron  or  steel),  which 
has  a piston  entering  through  its  head.  The  piston  is  gener- 
ally actuated  by  hydraulic  power,  and  serves  first  to  compress 
the  paste  and  then  to  force  it  through  a die  attached  to  the 
base  of  the  press. 


Fig.  5. 


SMOKELESS  POWDERS 


79 


To  prevent  clogging  of  the  dies  the  paste  is  first  forced 
through  a plate  perforated  with  very  fine  holes. 

By  varying  the  diameter  (or  form)  of  the  die  the  same 
press  may  be  used  for  pressing  and  molding  powders  for  use 
in  guns  of  all  calibers. 

In  case  of  powders  of  small  diameters,  such  as  filite,  cordite, 
etc.,  the  thread  or  cord  is  either  reeled  at  once,  as  it  emerges 
from  the  press,  on  drums,  and  the  drums  are  then  transferred 
to  the  drying  house,  where  they  remain  until  practically 
all  of  the  solvent  is  driven  off;  or  it  is  received  on  a canvas 
belt  which  passes  over  steam-heated  pipes  and  is  discharged 
into  wire  baskets,  which  are  subsequently  placed  in  the  dry- 
ing house  until  the  cord  or  thread  is  ready  for  granulation. 
For  small-arm  powder  the  threads  are  passed  under  revolving 
knives  and  cut  into  very  short  cylinders,  which  are  dusted 
and  sometimes  glazed  as  described  in  the  case  of  ordinary 
gunpowder.  The  diameters  of  powders  intended  for  guns  of 
larger  caliber  vary  according  to  the  gun,  and  the  grains  are 
both  perforated  and  cut  into  lengths  as  the  powder  emerges 
from  the  dies. 

Properties  of  Smokeless  Powders. — The  color  of  smoke- 
less powder  varies  from  a grayish  yellow  to  dark  brown,  and 
from  being  translucent  to  entire  opaqueness.  When  glazed 
they  resemble  ordinary  gunpowder,  except  in  form  of  grain, 
but  upon  cutting  through  the  grain  or  washing  off  the  graphite 
the  color  peculiar  to  the  composition  of  the  powder  is  readily 
seen.  In  texture  they  are  smooth,  and  are  either  very  hard 
and  brittle  or  they  are  tough  and  of  the  consistency  of  india- 
rubber.  They  are  insoluble  in  water  and  are  practically 
unaffected  by  it.  They  are  insensitive  to  shock  of  impact  or 
to  the  passage  of  a bullet  through  them.  They  are  more 
difficult  to  ignite  than  black  powder  and  charges  are  generally 
primed  with  the  latter  to  insure  ignition.  They  leave  very 
little  residue  in  the  bore  of  a gun. 


80 


GUNNERY 


Recapitulation. — 1.  Smokeless  powders  may  be  divided  into 
two  classes,  viz: 

(1)  Those  consisting  of  guncotton  alone. 

(2)  Those  consisting  of  guncotton  and  nitroglycerin. 

2.  In  both  classes  of  smokeless  powders  the  guncotton  is 
dissolved^  and  reduced  to  a gelatinized  mass  and  then  pressed 
into  grains  of  regular  shape. 

3.  The  form  of  grain  adopted  by  the  United  States  is  a 
cylinder  which  for  guns  of  small  caliber  has  but  one  central 
perforation,  while  the  grains  for  guns  of  larger  caliber  are 
multiperforated. 

4.  Smokeless  powders  differ  radically  from  ordinary  gun- 
powder in  physical  properties  as  well  as  in  their  composition. 

* The  substance  formed  by  dissolving  grmcotton  is  technically  called  a “colloid.” 
Colloids  when  ignited  even  in  a closed  chamber  do  not  explode,  but  bum  regu- 
larly in  parallel  surfaces.  It  is  this  property  of  colloids  that  renders  them  avail- 
able for  use  in  guns. 


CHAPTER  V 


EXPLOSIVE  COMPOUNDS— GUNCOTTON  AND 
NITROGLYCERIN 

As  gunpowder  is  the  best-known  example  of  explosive  mix- 
tures, so  guncotton  and  nitroglycerin  may  be  taken  as  the 
best  known,  and  with  their  derivatives  the  most  generally 
used  types  of  explosive  compounds. 

Guncotton. — As  its  name  implies,  this  is  an  explosive 
derived  from  cotton,  and  is  made  by  dipping  or  steeping 
pure  dry  cotton  in  a mixture  of  the  purest  and  strongest  nitric 
and  sulphuric  acids. 

The  purification  of  the  cotton  before  being  immersed,  the 
conversion  of  the  cotton  into  guncotton,  and  the  subsequent 
purification  of  the  guncotton  are  lengthy  processes  attended 
with  considerable  difiiculty,  and  requiring  complicated 
machines,  but  the  principles  governing  these  steps  are  easily 
understood. 

For  practical  reasons  the  cotton  used  in  the  manufacture 
of  guncotton  is  “cop  waste”  (or  “weaver’s  waste”),  which 
consists  of  the  tangled  clippings  from  the  spinning  rooms  of 
cotton-mills.  It  therefore  generally  contains  more  or  less 
oil,  dirt,  and  moisture  (water).  When  impure  or  unclean 
cotton  is  immersed  in  the  acid  mixture,  the  impurities  (oil, 
dirt,  etc.)  are  acted  upon  by  the  acids  and  form  compounds 
which  are  unstable  and  liable  to  explode  during  manufacture, 
and,  if  not  removed,  lead  to  the  subsequent  decomposition  of 
the  guncotton. 

The  presence  of  moisture  during  the  immersion  of  the  cotton 
serves  to  dilute  the  acid  mixture  and  to  cause  heat,^  which 

1 The  heat  is  caused  by  the  water  uniting  chemically  with  the  sulphuric  acid. 

81 


82 


GUNNERY 


also  gives  rise  to  the  formation  of  unstable  compounds, 
whose  action  is  as  just  described. 

The  use  of  weak  acids  or  too  short  an  immersion  prevents 
the  complete  conversion  of  the  cotton  into  the  highest  and 
most  stable  form  of  guncotton,  such  as  is  used  for  military 
purposes.^ 

Manufacture  of  Guncotton. — The  following  is  an  outline 
of  the  processes  of  manufacture  of  guncotton  followed  by 
the  best  factories  in  this  country  and  abroad: 

1.  The  “cop  waste”  is  first  thoroughly  cleansed  and  dried. 

2.  The  acids  are  mixed  in  the  proportions  of  1 part  of  nitric 
to  3 parts  of  sulphuric  ^ and  allowed  to  cool. 

3.  The  cotton  is  immersed  in  the  proportions  of  1 part 
of  cotton  to  10  parts  of  acid  for  the  period  of  ten  minutes. 

4.  Nearly  all  of  the  acid  is  squeezed  out  of  the  guncotton, 
which  is  next  placed  in  an  earthenware  crock  and  allowed 
to  remain  (“digest”)  for  twenty-four  hours. 

5.  All  remaining  traces  of  acid  are  removed  by  wringing, 
washing,  and  boiling  the  guncotton. 

6.  The  guncotton  is  reduced  to  the  fineness  of  corn  meal 
in  a machine  similar  to  an  ordinary  paper-pulping  ma- 
chine. 

7.  The  guncotton  pulp  is  washed,  first  in  fresh  water, 
and  then  in  water  containing  lime,  caustic  soda,  and  marble 
dust.  3 

8.  The  water  is  drawn  off  and  the  guncotton  drained  until 

^ When  cotton  is  acted  upon  by  mixtures  of  nitric  and  sulphmic  acid  various 
products  are  obtained,  nearly  all  of  which  are  more  or  less  explosive  and  more 
or  less  stable,  depending  upon  the  strength  of  the  acids  and  the  length  of  time 
the  cotton  is  subjected  to  their  action.  Only  the  highest  grade  of  guncotton, 
obtained  as  described  above,  is  sufficiently  stable  for  military  purposes.  This 
product  is  called  “trinitrocelluluse.” 

^ The  sulphuric  acid  is  added  to  absorb  any  original  moisture  present  in  the 
waste  or  nitric  acid,  as  well  as  the  water  formed  during  the  conversion,  so  as 
to  preserve  the  necessary  strength  of  the  nitric  acid. 

® This  last  solution  is  used  to  neutrahze  or  destroy  any  possible  trace  of  acid 
that  might  remain  in  the  guncotton. 


EXPLOSIVE  COMPOUNDS 


83 


it  contains  about  30  per  cent,  of  water,  and  in  this  condition 
is  stored  in  large  tanks  until  required  for  use. 

9.  As  found  in  the  service,  guncotton  is  packed  in  bulk  in 
boxes  containing  about  100  pounds,  or  in  molded  rectangular 
blocks  2.9  by  2.9  by  2 inches.  The  corners  of  the  blocks  are 
chamfered  and  each  block  is  perforated  through  the  center  to 
receive  a detonator. 

Properties  of  Guncotton. — The  fibrous  ^ guncotton  seen  in 
ordinary  light  differs  very  little,  if  any,  from  the  cotton  from 
which  it  is  made.  It  is  harsher  to  the  touch  and  less  flexible 
than  cotton;  when  dry,  it  becomes  highly  electrified  if  rubbed 
between  the  fingers,  and  is  luminous  when  rubbed  in  the  dark. 

Guncotton  is  completely  insoluble  in  water  and  is  said  to 
absorb  less  moisture  from  the  air  than  either  ordinary  cotton 
or  gunpowder. 

The  fibrous  guncotton  ordinarily  contains  from  1.5  to  2 
per  cent,  of  water  when  dry,  and  may  absorb  as  much  as  2.75 
per  cent,  of  moisture  without  having  any  of  its  properties 
impaired. 

A molded  block  of  guncotton  as  it  comes  from  the  press 
weighs  about  10  ounces,  and  contains  from  14  to  16  per 
cent,  of  water.  Before  being  sent  from  the  factory,  the  blocks 
are  soaked  in  fresh  water  until  they  cease  to  absorb  water,  ^ 
and  are  packed  directly  in  the  torpedo  cases. 

If  a flame  or  any  incandescent  body  be  brought  into  con- 
tact with  dry,  loose  guncotton,  the  latter  burns  with  a flash 
but  without  explosion.  A block  of  compressed  guncotton 
may  be  safely  ignited  in  the  hand,  placed  on  the  ground,  and 
the  flame  extinguished  by  pouring  water  on  it;  but  if  a very 
large  mass  of  guncotton  be  ignited,  an  explosion  may  result 
from  the  intense  heat  of  the  burning  portion  raising  the 

^ Fibrous  guncotton  is  the  product  before  passing  through  the  pulping  machine 
and  being  cut  up  or  reduced. 

^ They  then  contain  about  35  per  cent,  of  water,  and  can  be  exploded  only  by 
the  detonation  of  dry  blocks  placed  in  contact  with  them. 


84 


GUNNERY 


temperature  of  the  rest  up  to  its  point  of  explosion,  while  at 
the  same  time  acting  as  a partial  confinement  to  the  un- 
ignited portion.  The  exploding  point  of  guncotton  is  about 
360°  F. 

To  develop  the  force  of  guncotton  it  must  be  strongly 
confined  when  detonated,  and  unless  so  confined  it  is  not 
particularly  sensitive  to  friction,  percussion,  pressure  or  shock. 
Cold  has  no  effect  on  guncotton  unless  sufficiently  intense  to 
freeze  the  water  contained  in  it.  The  effect  of  freezing  on 
wet  compressed  guncotton  is  to  cause  flaking,  cracking,  and 
breaking  or  crumbling  of  the  block,  which  is  to  be  avoided 
if  possible.  While  guncotton  is  one  of  the  most  powerful 
explosives,  and  necessarily  dangerous  as  all  explosives  are, 
when  handled,  stored,  and  used  as  directed,  it  is  the  safest 
explosive  known,  and  is  especially  adapted  for  use  for  mihtary 
purposes. 

Decomposition  of  Guncotton. — When  properly  made  gun- 
cotton is  almost  entirely  free  from  any  tendency  to  undergo 
dangerous  decomposition.  The  decomposition  (deterioration) 
of  guncotton  is  caused  primarily  by  the  action  of  any  free 
acid  that  may  be  present  (in  the  product)  due  to  imperfect 
washing  of  the  product  after  conversion,  or  to  the  presence 
of  impurities  due  to  imperfect  cleansing  of  the  cotton  before 
conversion  or  to  incomplete  conversion.  The  action  of  the 
acid  is  accelerated  and  intensified  by  heat. 

When  guncotton  is  decomposing  it  first  begins  to  give 
off  deep  brownish-red  fumes,  and  at  the  same  time  it  begins 
to  show  pasty  yellow  spots,  and  eventuallj’’  the  whole  becomes 
converted  into  a pasty  yellow  mass  which  first  shrinks  to 
about  one-tenth  of  the  volume  of  the  original  guncotton, 
and  then  swells  up  as  the  gas  is  evolved.  During  the  next 
stage  the  guncotton  again  shrinks  and  is  converted  into  a 
gummy  residue,  which  finally  dries  up  to  a brown  horn-like 
mass.  Heat^  is  produced  during  decomposition,  and  if  the 

^ This  heat  is  due  to  chemical  action. 


EXPLOSIVE  COMPOUNDS 


85 


guncotton  is  confined  the  heat  generated  may  raise  its  tem- 
perature up  to  its  exploding  point  and  cause  an  explosion. 

To  produce  this  result  in  wet  guncotton  it  is  necessary 
that  the  amount  of  acid  present  should  be  very  much  in  excess 
of  the  guncotton  with  which  it  is  in  contact,  while  the 
water  present  tends  to  prevent  any  considerable  rise  in  tem- 
perature. 

Nitroglycerin. — In  its  composition  and  structure  glycerin  is 
chemically  analogous  to  cotton,  and  nitroglycerin  is  derived 
from  the  former  in  exactly  the  same  manner  that  gimcotton 
is  obtained  from  the  latter. 

Nitroglycerin  is  an  explosive  compound  made  by  acting 
upon  pure  anhydrous^  glycerin  with  a mixture  of  the  purest 
and  strongest  nitric  and  sulphuric  acids. 

The  considerations  which  require  absolutely  pure  and  dry 
materials  in  the  manufacture  of  guncotton  apply  with  equal 
force  in  making  nitroglycerin.  ^ 

Sobrero,  the  discoverer  of  nitroglycerin,  proposed  the  fol- 
lowing process  for  making  this  explosive:  “Pour  3^2  ounce  of 
anhydrous  glycerin,  with  constant  stirring,  into  a mixture  of  2 
ounces  of  concentrated  sulphuric  acid,  and  1 ounce  of  fuming 
nitric  acid.” 

Manufacture  of  Nitroglycerin. — The  following  is  an  out- 
line of  the  manufacture  of  nitroglycerin  by  all  large  dynamite 
makers^  in  this  country. 

1.  About  600  pounds  of  nitric  acid  and  1,100  pounds  of 
sulphuric  acid  are  mixed  in  a leaden  tank  and  allowed  to  cool 
for  twelve  hours. 

2.  This  mixture  (about  1,700  pounds)  is  run  into  the 

^ A substance  is  said  to  be  anhydrous  when  it  is  entirely  free  from  moisture. 

^ It  is  the  presence  of  fatty  impurities  in  the  glycerin  that  gives  rise  to  the  for- 
mation of  unstable  bodies,  which  cause  the  decomposition  and  so-called  spon- 
taneous explosion  of  nitroglycerin.  The  presence  of  water,  or  the  use  of  weak 
acids,  acts  as  described. 

^ This  process  is  known  as  the  “Mowbray  method  of  making  nitroglycerin,” 
having  been  introduced  into  this  coimtry  by  Mr.  Mowbray. 


86 


GUNNERY 


mixing  apparatus/  and  into  it  is  injected  in  the  form  of  spray 
the  charge  of  glycerin  (about  240  pounds)/ 

3.  After  the  entire  charge  of  glycerin  has  been  introduced 
it  is  allowed  to  remain  in  the  mixing  apparatus  for  a few 
minutes,  and  the  nitroglycerin  which  appears  on  the  surface 
is  then  separated  from  the  acid  mixture. 

4.  The  nitroglycerin  is  next  thoroughly  washed  with  fresh 
water  until  it  shows  no  trace  of  acidity. 

5.  To  neutralize  (or  destroy)  the  effect  of  any  traces  of 
acid  which  may  not  have  been  removed  by  the  last  washing, 
the  explosive  is  next  washed  with  a solution  of  carbonate  of 
soda  in  water  until  it  shows  a distinct  alkaline  reaction.  ^ 

6.  The  nitroglycerin  in  transferred  from  the  washing  appa- 
ratus, through  coarse  muslin  filters,  to  the  storage  tanks, 
where  it  is  kept  generally  under  water. 

The  French  method  of  making  nitroglycerin  differs  in  prin- 
ciple from  that  just  described.  In  this  process  two  mixtures 
are  made,  one  of  equal  parts  of  nitric  and  sulphuric  acids, 
the  other  a mixture  of  1 part  of  glycerin  and  about  3 parts 
of  sulphuric  acid. 

Both  mixtures  are  allowed  to  cool  and  are  then  mixed  in 
the  proportions  of  about  5|  parts  of  the  first  to  about  4 parts 
of  the  second  and  the  conversion  allowed  to  proceed  by  itself. 
About  twelve  hours  are  required  for  the  complete  conversion 
of  300  pounds  of  glycerin  by  this  process. 


^ The  mixing  apparatus  consists  of  a large  cast-iron  tank  filled  with  water 
and  containing  a smaller  iron  tank  in  which  the  materials  are  mixed.  The  latter 
contains  leaden  “worms”  (or  spiral  pipes)  through  which  cold  water  is  made 
to  circulate  during  the  mixing. 

^ This  step  is  attended  with  the  evolution  of  considerable  heat,  which,  unless 
regulated,  is  hable  to  “fire”  the  charge.  It  is  therefore  necessary  to  watch  a 
thermometer  (the  bulb  of  which  is  immersed  in  the  mixture)  carefully,  and 
should  the  temperature  rise  above  80°  F.,  the  introduction  of  the  glycerin  is 
stopped. 

^ The  presence  of  acid  in  a solution  is  shown  by  the  color  of  blue  htmus  paper 
being  changed  to  red  when  dipped  in  it.  If  a solution  is  alkaline,  the  color  of 
red  litmus  paper  is  changed  to  blue. 


EXPLOSIVE  COMPOUNDS 


87 


Properties  of  Nitroglycerin. — Freshly  made  by  the  Mow- 
bray process,  nitroglycerin  is  a creamy  white,  opaque,  oily 
liquid,  but  upon  standing  for  a time,  the  length  of  which 
depends  upon  the  temperature,  it  “clears”  or  becomes  trans- 
parent and  colorless,  or  nearly  so.  As  found  in  commerce 
it  has  a yellow  or  brownish-yellow  color.  Although  very 
slightly  soluble  in  it,  it  does  not  mix  with  and  is  unaffected 
by  cold  water.  It  has  a sweet,  pungent,  aromatic  taste,  and 
is  an  active  'poison,  so  that  mere  contact  with  it  will  induce 
in  most  persons  a violent  sickness,  and  an  especially  painful 
form  of  headache.^  Freshly  made  opaque  nitroglycerin  freezes 
at  about  — 4°  F.,  and  the  transparent  explosive  at  about  40°  F., 
in  both  cases  freezing  to  a white  crystalline  mass;  and  once 
frozen  it  remains  in  this  condition  even  when  exposed  for 
some  time  to  a temperature  above  its  freezing-point. 

Pure  nitroglycerin  is  not  sensitive  to  friction  or  moderate 
percussion,  except  when  pinched  between  metallic  surfaces.^ 
When  confined  and  struck  a smart  blow  it  explodes  on 
account  of  its  incompressibility;  when  in  a state  of  decom- 
position, however,  it  is  much  more  sensitive  and  explodes 
upon  being  struck  even  if  unconfined. 

The  firing-point  of  nitroglycerin  is  about  356°  F.  Uncon- 
fined and  freely  exposed  to  a flame  nitroglycerin  burns  with 
a brilliant  flame,  but  without  explosion.  In  a frozen  state 
nitroglycerin  becomes  insensitive  to  nearly  all  kinds  of  shock, 
but  at  the  same  time  loses  in  a great  measure  its  explosive 
power,  and  it  should  therefore  be  thawed  before  being 
used. 

Most  of  the  accidents®  that  have  occurred  with  nitrogly- 

^ Strong  black  coffee  is  recommended  as  an  antidote. 

® A quantity  of  nitroglycerin  has  been  thrown  up  by  means  of  a rocket  to  a 
height  of  1,000  feet,  whence  it  fell  without  explosion  upon  impact. 

^ One  very  frequent  source  of  accident  results  from  carelessly  allowing  cans 
or  other  vessels  in  which  nitroglycerin  has  been  stored  to  lie  around  loosely. 
In  nearly  every  case  particles  of  the  explosive  adhere  to  the  vessels  and  are 
exploded  by  a chance  blow.  All  such  vessels  should  be  destroyed  immediately. 


88 


GUNNERY 


cerin  have  resulted  from  carelessness  in  thawing  the  explo- 
sive. 

How  to  Thaw  Nitroglycerin  when  Frozen. — When  frozen, 
nitroglycerin  may  be  conveniently  and  safely  thawed  by  plac- 
ing the  vessel  containing  it  in  another  vessel  containing  water 
not  hotter  than  the  hand  can  bear  (about  100°  F.)  and  allow- 
ing it  to  remain,  replenishing  the  warm  water  when  necessary, 
until  the  explosive  is  thawed.  Under  no  circumstances  should 
frozen  nitroglycerin  be  put  in  the  same  vessel  as  the  water, 
nor  should  it  be  placed  near  an  open  fire  nor  in  contact  with 
any  heated  surface,  nor,  in  short,  thawed  in  any  other  way 
than  as  just  directed. 

Decomposition  of  Nitroglycerin. — Pure  nitroglycerin  does 
not  spontaneously  decompose  at  any  ordinary  temperature, 
but,  as  in  the  case  of  guncotton,  the  presence  of  free  acid 
combined  with  heat  quickly  leads  to  its  decomposition.  High 
temperature  alone  does  not  injure  thoroughly  purified  nitro- 
glycerin, and  the  presence  of  any  acid  is  determined  by  shak- 
ing a few  drops  in  water  and  testing  the  water  with  blue 
litmus  paper.  Wliile  undergoing  decomposition  nitrogly- 
cerin becomes  exceedingly  dangerous,  the  slightest  shock 
causing  violent  explosion;  but  unless  a very  large  quantity 
is  involved  serious  accidents  can  be  prevented  by  exercising 
ordinary  care.  Decomposition  of  nitroglycerin  is  detected 
by  the  acid  reaction  on  litmus  paper  and  expecially  by  the 
explosive  becoming  greenish  in  appearance.  WTien  in  this 
condition  nitroglycerin  should  be  very  carefully  removed  and 
exploded. 

Recapitulation. — 1.  Guncotton  is  an  explosive  compound 
made  by  immersing  pure  dry  cotton  in  a mixture  of  the  purest 
and  strongest  nitric  and  sulphuric  acids. 

2.  The  best  proportions  of  the  acids  in  the  mixture  are  1 
part  of  nitric  acid  to  3 parts  of  sulphuric  acid,  while  those  of 
the  cotton  and  the  mixture  are  1 part  of  the  former  to  10 
parts  of  the  latter. 


EXPLOSIVE  COMPOUNDS 


89 


3.  The  several  steps  in  the  manufacture  of  guncotton 
have  for  their  objects: 

(1)  The  thorough  drying  and  cleansing  of  the  mate- 

rials. 

(2)  The  complete  conversion  of  the  cotton  into  gun- 

cotton. 

(3)  The  removal  of  every  trace  of  free  acid  from  the 

guncotton. 

4.  Guncotton  is  one  of  the  safest  explosives  known,  being 
absolutely  inexplosive  when  it  contains  30  per  cent,  of  water, 
and  is  an  excellent  service  explosive, 

5.  Nitroglycerin  is  an  explosive  compound  obtained  from 
the  action  of  a mixture  of  the  purest  and  strongest  nitric  and 
sulphuric  acids  upon  pure  anhydrous  glycerin. 

6.  The  proportions  of  acids  in  the  mixture  are  1 part  of 
nitric  acid  to  2 parts  of  sulphuric  acid,  while  those  of  the  gly- 
cerin and  the  mixture  are  about  1 part  of  the  former  to  4 
or  5 parts  of  the  latter. 

7.  Thoroughly  purified  nitroglycerin  is  comparatively  safe 
(unless  frozen),  and  not  liable  to  undergo  decomposition. 

8.  When  frozen,  nitroglycerin  becomes  dangerously  sensi- 
tive, and  it  should  be  thawed  only  in  the  manner  prescribed. 

9.  Both  guncotton  and  nitroglycerin  are  liable  to  decom- 
pose when  they  contain  free  acid  and  are  exposed  to  high 
temperatures. 

10.  When  found  to  be  decomposing  these  explosives 
should  be  carefully  removed  and  immediately  exploded. 


CHAPTER  VI 


GUNCOTTON  POWDERS.  DYNAMITE. 
DETONATORS 

Guncotton  and  nitroglycerin  are  the  most  powerful 
known  explosives  and,  on  account  of  their  tremendous  explo- 
sive force,  are  unsuitable  for  many  military  and  industrial 
purposes.  In  order  to  modify  and  regulate  their  action  they 
are  mixed  with  other  substances,  the  resulting  mixtures  being 
known  as  guncotton  powders  and  dynamite. 

Dynamite. — At  present  dynamite  is  a generic  term  and 
includes  all  explosives  made  hy  absorbing  liquid  nitroglycerin 
in  solid  materials  which  are  capable  of  retaining  it. 

The  solid  material  used  to  absorb  nitroglycerin  (or  the 
absorbent)  is  technically  called  the  ‘‘dope.” 

The  absorbent  may  be  entirely  inert  and  used  to  convert 
nitroglycerin  from  the  liquid  into  the  solid  form,  or,  on  the 
other  hand,  it  may  itself  be  an  explosive.  In  the  first  case 
the  explosive  force,  bulk  for  bulk,  of  the  resulting  explosive 
will  be  diminished,  whereas  in  the  second  case  it  will  be 
increased. 

Kieselguhr  Dynamite  or  Giant  Powder. — This  is  one  of 
the  earliest  and  best-known  forms  of  dynamite,  and  consists 
essentially  of  a mixture  of  kieselguhr^  and  nitroglycerin,  to 
which  is  added  a very  small  percentage  of  sodium  (or  other 
alkaline)  carbonate  to  neutralize  any  traces  of  free  acid  that 
may  remain  in  the  nitroglycerin. 

^Kieselguhr  is  one  of  the  best-known  “dopes,”  being  perfectly  inert  and  pos- 
sessing very  high  absorptive  power,  the  best  varieties  being  able  to  absorb  and 
retain  82  per  cent,  of  nitroglycerin.  It  is  largely  organic  in  its  composition, 
containing  decomposed  shells  of  mjTiads  of  diatoms,  which  preserve  their  cellu- 
lar formation  even  after  calcination. 


90 


GUNCOTTON  POWDERS 


91 


The  kieselguhr  is  first  calcined,  pulverized,  and  thoroughly 
dried.  It  is  then  weighed  and  put  into  the  mixing  troughs. 

The  nitroglycerin  is  brought  to  the  mixing  house  in  gutta- 
percha or  lacquered  wood-pulp  buckets  and  poured  directly 
upon  the  absorbent,  or  it  may  be  brought  to  the  troughs 
through  stout  rubber  hose. 

The  proportions  vary  with  the  grade  of  dynamite  required. 

The  mixing  is  done  entirely  by  hand,  the  workmen  wearing 
usually  india-rubber  gloves  during  the  operation.  After  the 
nitroglycerin  has  been  entirely  absorbed,  the  dynamite  is 
rubbed  through  wire  sieves  so  as  to  distribute  the  nitrogly- 
cerin uniformly  throughout  the  mass. 

Properties  of  Dynamite. — Kieselguhr  dynamite  is  a gran- 
ular substance,  the  color  of  which  varies  from  pearl-gray  to 
reddish-brown;  it  is  of  the  plastic  consistency  of  moist  clay. 
It  should  not  feel  greasy  to  the  touch,  nor  should  there 
be  any  trace  of  free  nitroglycerin  on  the  sides  of  the  con- 
taining box  or  cartridge  wrapper.  Dynamite  possesses  the 
physical  properties  of  nitroglycerin  and  is  therefore  equally 
poisonous.  Its  firing-point  is  about  356°  F.,  and  at  this 
temperature  it  either  burns  or  explodes;  if  free  from  pressure, 
confinement,  jar,  or  vibration,  it  burns;  otherwise  it  explodes. 
High  temperatures  below  its  firing-point  cause  dynamite 
“to  leak,”  that  is,  the  nitroglycerin  exudes  from  the  base 
(or  dope).  When  this  occurs  the  danger  attending  liquid 
nitroglycerin  is  ever  present.  Dynamite  freezes  at  about  40° 
F.,  and,  once  frozen,  it  remains  in  this  condition  at  tempera- 
tures considerably  above  its  freezing-point.  Although  less 
sensitive  when  frozen,  the  fact  that  it  is  still  a “high  explo- 
sive” must  always  be  remembered.  Wlien  frozen  it  can  be 
detonated  only  with  difficulty  and  always  with  greatly  dimin- 
ished force.  It  is  therefore  recommended  to  thaw  frozen 
dynamite  before  using  it. 

All  nitroglycerin  preparations,  when  heated  gradually  up 
to  their  exploding  points,  become  dangerously  sensitive  to  the 


92 


GUNNERY 


slightest  shock  or  blow,  and,  once  that  point  is  reached,  they 
no  longer  ignite  but  explode  violently ; and  further,  on  account 
of  the  poor  conductivity  of  the  material,  a very  small  portion 
of  dynamite  in  contact  with  the  source  of  heat  may  reach 
this  point  and  cause  the  explosion  of  the  rest  of  the  mass, 
which  may  be  considerably  below  the  danger  point. 

How  to  Thaw  Dynamite  When  Frozen. — The  best  way  to 
thaw  frozen  dynamite  is  to  open  the  packages  carefully  and 
place  them  in  a room  where  the  temperature  does  not  exceed 
150°  F.,  and  allow  the  explosive  to  thaw  gradually.  A room 
heated  by  steam  is  to  be  preferred. 

If  there  is  not  time  to  follow  this  method,  the  best  way  is 
to  place  the  cartridges  in  a water-tight  can,  and  suspend 
this  can  in  another  vessel  containing  water  not  hotter  than 
the  hand  can  bear. 

Under  no  circumstances  should  an  attempt  be  made  to 
thaw  any  form  of  dynamite  by  placing  it  near  a hot  fire,  nor 
directly  on  a hot  shovel  or  plate;  nor  by  leaning  it  against 
hot  brickwork,  steam  boilers,  or  radiators;  in  short,  never 
attempt  to  thaw  dynamite  in  any  other  way  than  as  indicated 
above. 

Explosive  Gelatin. — This  explosive  is  made  by  dissolving 
the  soluble  variety  of  guncotton  in  nitroglycerin.  For  mih- 
tary  purposes  the  proportions  of  the  ingredients  are  about 
4 parts  of  guncotton  to  92  parts  of  nitroglycerin,  to  which 
are  added  4 parts  of  camphor.  The  camphor  is  added  to  increase 
the  elasticity  and  solidity  of  the  explosive,  while  at  the  same 
time  it  reduces  its  sensitiveness.  As  might  be  expected  from 
combining  the  two  strongest  known  explosives,  the  resulting 
compound  is  the  most  powerful  form  of  dynamite. 

Properties  of  Explosive  Gelatin. — Explosive  gelatin  has 
the  appearance  of  a jelly-like  paste,  which  has  a honey- 
yellow  color,  and  a consistency  varjdng  from  tough  leather 
to  ordinary  jelly.  It  does  not  absorb  water,  and  when  placed 
in  it  only  a very  small  quantity  of  nitroglycerin  is  dissolved 


GUNCOTTON  POWDERS 


93 


from  the  surface,  which  assumes  a whitish  color,  but  no 
further  change  occurs,  no  matter  how  long  the  explosive 
remains  immersed.  Unconfined,  it  burns,  when  ignited, 
with  a bright  yellow  flame  and  a hissing  sound,  but  does  not 
explode.  If,  however,  it  is  confined  and  heated  to  its  ignition 
point,  it  explodes  violently. 

Heated  slowly,  it  explodes  at  about  399°  F.;  heated  rap- 
idly, it  explodes  at  464°  F.  The  exact  temperature  at  which 
explosive  gelatin  freezes  is  not  definitely  known,  but  it  is 
probably  about  40°  F.  When  frozen,  it  assumes  a crystalline 
structure  and  a somewhat  paler  yellow  color  than  when  in 
its  normal  condition.  Unlike  the  dynamites  previously 
mentioned,  explosive  gelatine  is  much  more  sensitive  to  shock 
when  frozen  than  when  in  the  unfrozen  state,  and  is  readily 
exploded  by  the  impact  of  bullets.  When  unfrozen,  it  is 
comparatively  insensitive  to  friction,  blows,  etc. 

On  account  of  its  solid  form  and  plastic  nature,  its  great 
power  and  comparative  safety,  explosive  gelatin  has  been 
regarded  as  the  ideal  military  explosive. 

The  original  and  best  grade  of  explosive  gelatin  is  manu- 
factured by  the  Nobel  Explosive  Company  of  Great  Britain. 
The  gelatin  manufactured  by  the  Forcite  Powder  Company 
in  this  country  is  similar  in  many  respects  to  the  Nobel  gela- 
tin, but  the  samples  tested  seem  to  have  a greater  tendency 
‘To  leak.” 

Detonators. — In  order  to  develop  the  full  force  of  gun- 
cotton, nitroglycerin,  and  explosives  derived  from  them,  they 
should  be  detonated. 

The  best-known  substance  to  cause  such  explosives  to 
detonate  is  mercury  fulminate. 

Mercury  fulminate  is  itself  an  explosive,  and  when  dry 
is  very  sensitive  to  all  kinds  of  shocks,  and  explodes  violently 
when  struck,  or  rubbed  or  pressed  between  hard  surfaces, 
or  when  heated.  When  moistened  so  as  to  contain  about 
30  per  cent,  of  water  it  is  practically  inexplosive.  Its  most 


94 


GUNNERY 


valuable  property  for  military  purposes  is  that  it  invariably 
causes  ‘'high  explosives”^  to  detonate  when  itself  exploded  in 
contact  with  or  very  near  such  substances.  When  used  for  this 
purpose  it  is  mixed  with  other  substances,  the  usual  mixture 
being  75  parts  of  mercury  fulminate  and  25  parts  of  potas- 
sium chlorate,  to  which  is  added  a little  ground  glass. 

The  detonator  case  is  a copper  capsule  about  IJ  inches  in 
length  and  | inch  in  diameter. 

The  decomposition  is  rubbed  very  fine  under  water,  par- 
tially dried  and  pressed  into  the  capsule,  where  it  dries  thor- 
oughly and  is  covered  with  a drop  of  varnish  or  a thin  disk 
of  foil. 

According  to  the  amount  of  fulminate  they  contain, 
detonators  are  graded  into  single,  double,  treble,  etc.,  force 
cays.  Single  force  caps  contain  3 grains,  double  6 grains,  etc., 
up  to  the  strongest  or  quintuple  force  cap,  which  contains 
15  grains  of  fulminate.  Detonators  are  made  so  as  to  be  fired 
by  means  of  a “time  fuse”  or  by  electricity.  The  ends  of 
detonators  to  be  fired  by  time  fuse  are  left  open  to  receive 
the  fuse,  while  electric  detonators  are  closed  by  means  of  a 
plug  made  of  sulphur  and  ground  glass,  through  which  pass 
two  wires.  The  ends  of  the  wires  are  connected  by  a very 
fine  wire  (or  bridge)  around  which  is  wrapped  a wisp  of  dry 
guncotton.  Wlien  the  electric  current  passes  through  the 
bridge  it  heats  it  and  the  guncotton  is  ignited  and  causes 
the  fulminate  to  detonate. 

Recapitulation. — 1.  On  account  of  their  tremendous  force, 
guncotton  and  nitroglycerin  are  combined  with  other  sub- 
stances to  modify  and  regulate  their  action,  the  resulting 
explosives  being  known  as  guncotton  powders  and  dynamite. 

2.  Dynamite  is  a term  which  includes  all  explosives  made 
by  absorbing  liquid  nitroglycerin  in  a sohd  material,  the 
absorbent  being  technically  known  as  the  “dope.” 

^ This  term  includes  guncotton,  nitroglycerin,  their  derivatives,  and  prac- 
tically all  explosives  capable  of  detonating. 


GUNCOTTON  POWDERS 


95 


3.  Dynamite  is  made  under  various  names  and  in  many 
grades,  the  strength  of  any  particular  grade  depending  upon 
the  amount  of  nitroglycerin  it  contains. 

N.  B. — For  demolitions,  submarine  mines,  and  military 
purposes  in  general,  only  the  highest  grade  or  strongest 
dynamite  should  be  used. 

4.  All  guncotton  powders  and  dynamite  (“high  explo- 
sives”) should  be  exploded  by  means  of  detonators. 

5.  Detonators  (or  “blasting  caps”)  may  be  fired  by  a 
“time  fuse”  or  by  electricity. 

6.  The  rate  of  burning  of  a time  fuse  should  always  be 
determined  before  it  is  used. 

7.  Dynamite  should  never  be  used  when  frozen,  and  great 
precaution  should  be  used  when  it  is  thawed. 


I 


PART  III 


BALLISTICS 

Chapter  I.  Ballistics. 

Chapter  II.  Interior  Ballistics. 
Chapter  III.  Exterior  Ballistics. 


BALLISTICS 


CHAPTER  I 
BALLISTICS 

Gravity. — If  a ball  be  thrown  straight  upward  it  will 
rise  with  decreasing  rapidity  to  an  elevation  depending  upon 
the  energy  with  which  it  is  thrown.  This  energy  is  the  force 
of  propulsion.  If  there  were  no  such  things  as  gravity  and 
atmospheric  resistance  the  ball  would  continue  to  rise  indefi- 
nitely and  would  pass  on  to  a point  infinitely  remote  from 
the  earth. 

We  are  aU  familiar  with  the  action  of  a magnet  upon  a 
nail.  The  pull  of  the  magnet  is  called  magnetic  attraction. 
Let  us  suppose  that  an  immense  magnet  is  located  at  the 
center  of  the  earth  with  a power  of  attraction  sufficient  to 
draw  objects  hurled  in  the  air  back  to  the  earth’s  surface. 
Such  a force  would  correspond  to  what  is  known  as  gravity. 

Gravity  then  is  the  force  exerted  upon  any  faffing  mass 
produced  by  the  earth’s  attraction,  and  it  is  this  attraction 
which  gives  weight  or  the  quality  of  heaviness  to  every  tangi- 
ble object. 

The  force  of  gravity  is  constantly  exerted,  so  that  when  the 
ball  is  hurled  upward  gravity  opposes  the  force  of  propulsion 
until  the  latter  is  entirely  overcome.  When  the  ball  no  longer 
rises  and  yet  has  not  begun  to  fall,  the  two  forces  are  bal- 
anced, or  an  equilibrium  has  resulted. 

Gravity  alone,  however,  has  not  brought  the  ball  to  rest. 
Another  force,  known  as  atmospheric  resistance,  has  assisted 
the  pull  of  the  earth  to  counteract  the  force  of  propulsion. 


100 


GUNNERY 


Atmospheric  Resistance. — The  atmosphere  is  the  mass  of 
aeriform  fluid  or  air  surrounding  the  earth.  It  is  a tangible 
substance  and,  therefore,  has  a definite  weight,  being  less 
dense  or  lighter  at  higher  elevations,  than  at  the  earth’s 
surface. 

The  weight  of  the  atmosphere  at  sea  level  is  14.7  pounds 
per  square  inch  of  surface,  and  the  force  which  the  atmos- 
phere exerts  in  all  directions  is  known  as  atmospheric  pres- 
sure. This  pressure  and  the  resistance  of  the  atmosphere 
both  resisted  the  rise  of  the  ball.  Without  the  opposition 
of  gravity  and  the  resistance  of  the  atmosphere  the  ball 
would  have  continued  upward  indefinitely,  for  the  force  of 
propulsion  would  never  have  been  overcome,  since  nothing 
would  have  opposed  it. 

Trajection. — The  act  of  casting  a body  through  the  air 
is  called  trajection.  Hence  the  course  which  a body  describes 
in  passing  through  space  is  called  the  trajectory. 

From  the  earliest  times  the  method  of  fighting  by  hurling 
objects  at  an  enemy  has  been  employed.  This  method 
obviously  possesses  the  merit  of  enabling  one  to  strike  an 
enemy  from  a distant  and  possibly  a safe  point,  pro\fided 
sufficient  skill  in  trajection  is  possessed.  This  necessary 
element  of  skill  caused  the  Latins  to  term  the  method  an  art 
{ars,  artis) , from  which  they  named  their  mechanical  appli- 
ances employed  therein,  artillaria.  In  a general  sense  the 
name  covered  all  weapons  employed  for  trajection.  Hence 
it  was  formerly  used  for  bows  and  arrows.  (I.  Sam.  xx,  40). 
From  the  Latin  word  came  the  French  artillerie,  which  through 
modern  developments  applies  only  to  the  various  tj^Des  of 
cannon. 

Artillery,  as  a name,  no  longer  has  a modern  application, 
for,  in  the  strictest  sense,  the  method  of  trajection  now 
employed  is  not  an  art  but  a science.  The  word  science  means 
knowledge;  comprehension  or  understanding  of  the  truths 
or  facts  of  any  subject.  Had  the  Latins  amassed  a great 


BALLISTICS 


101 


knowledge  of  trajection  by  severely  testing  its  possibilities 
as  a method  of  warfare;  had  they  coordinated  and  systema- 
tized the  practice  with  regard  to  the  laws  and  forces  of  nature, 
they  would,  no  doubt,  have  derived  a name  for  their  machinery 
from  the  word  scientia  instead  of  from  the  word  ars. 

The  foregoing  digression  has  been  indulged  in  with  a pur- 
pose, for  it  is  all-important  for  the  artillerist  to  realize  at 
the  start  that  his  profession  is  a science,  in  the  practice  of 
which  his  natural  qualifications  may  assist,  but  cannot  alone 
make  him  proficient,  as  in  the  case  of  an  artist. 

In  our  modern  field  artillery  the  shell  and  the  shrapnel 
have  been  substituted  for  the  arrow  and  the  stone  of  the 
ancients;  gunpowder  has  replaced  the  bow  and  the  sling. 
But  the  natural  laws  of  trajection  remain  the  same,  for  the 
forces  of  nature  are  immutable.  The  course  described  by 
the  stone  tossed  from  the  primitive  catapult  is  but  the  tra- 
jectory of  our  steel  projectile.  In  the  former  case  a spring 
and  lever  supplied  the  force  of  propulsion,  in  the  latter  we 
use  gunpowder.  And  so  a rough  art  has  become  an  intricate 
and  highly  developed  science. 


DEVELOPMENT  OF  FIELD  ARTILLERY 

It  may  be  interesting  to  note  here  a few  facts  in  connection 
with  the  ancient  art  of  trajection,  in  which  the  science  of 
ballistics  originated.  We  wiU  begin  at  a time  when  the  ancient 
machinery  began  to  be  rapidly  developed  into  effective  engines 
of  war. 

The  existing  artillery  was  much  improved  by  Philip  and 
later  by  the  young  Alexander,  the  latter  being  the  Langlois 
of  the  ancients.  He  was  the  first  to  give  the  machines  suffi- 
cient mobility  to  make  them  available  in  the  field.  Hitherto 
they  had  only  been  used  in  sieges,  but  Alexander  placed  them 
on  wheels  and  caused  the  light  artillery  to  accompany  the 


102 


GUNNERY 


foot  and  mounted  troops,  thus  making  of  it  a third  arm  of 
the  mobile  army.  Philip  and  Alexander  also  gave  to  this 
branch  of  the  service  its  battery  formation.  At  one  time 
Philip  had  one  hundred  and  fifty  companies  on  foot  and  twenty- 
five  reserve  batteries  in  his  arsenals. 

The  catapult  was  the  invention  of  the  Syrians,  according 
to  Pliny.  It  consisted  of  a huge  bow  mounted  on  a platform, 
the  propelling  force  usually  being  obtained  by  a twisted  cord 
or  gut  applied  to  the  arms  of  the  bow.  The  bowstring  was 
tightened  by  a windlass  and  released  by  a spring.  The  cata- 
pult shot  huge  iron-pointed  arrows  or  pikes  weighing  from 
ten  to  three  hundred  pounds,  which  had  considerable  pene- 
trative power.  It  was  capable  of  carrjdng  nearly  one-hah 
mile,  and  was  accurate  to  five  hundred  paces. 

The  ballista  was  originated  by  the  Phoenicians.  It  threw 
stones  up  to  fifty  pounds  in  weight  and  over,  and  was  the 
mortar  of  the  ancients.  The  missile  could  be  cast  about 
half  a mile.  It  consisted  of  a stout  beam  or  arm  of  wood  one 
end  of  which  bore  a spoon  or  bowl  in  which  was  held  the 
stone,  while  the  other  end  was  secured  by  a twisted  cord 
or  gut  mounted  in  a timber  frame.  Being  brought  backward 
against  the  twist  to  a nearly  horizontal  position  by  a wind- 
lass, and  the  stone  or  projectile  placed  m the  spoon  or  bowd, 
the  arm  was  suddenly  released  and  flew  upw’ard  with  great 
power.  Its  motion  was  suddenly  arrested  by  an  upper  trans- 
verse beam,  or  by  cords  fastened  to  the  framewmrk.  The 
projectile  left  the  spoon  at  this  point  and  could  be  directed 
with  considerable  accuracy.  Red-hot  balls  and  fii’e-pots  were 
also  hurled  by  the  ballista,  and  sometimes  iofected  corpses 
were  thrown  into  a besieged  city  to  spread  disease. 

The  Macedonian  artillery  was  extremely  efi’ective  in  the 
hands  of  Alexander,  who,  like  Napoleon  many  centuries  later, 
appreciated  the  great  value  of  his  artillery.  In  transporting 
the  machines  the  Macedonians  carried  only  the  essential 
parts,  for  the  heavy  timbers  could  be  cut  and  fitted  in  any 


BALLISTICS 


103 


place  where  trees  were  accessible.  A horse  or  a mule  could 
transport  the  essentials  of  one  balhsta  or  catapult  such  as 
they  were  when  perfected  by  Alexander’s  engineers. 

Caesar  also  made  constant  use  of  the  catapult  and  the 
baUista.  In  his  day  the  larger  variety  of  catapult  was  capa- 
ble of  projecting  heavy  beams  a horizontal  distance  of  four 
hundred  to  eight  hundred  paces.  The  small  or  mobile  cata- 
pult (scoT'pio)  shot  heavy  lances  three  to  five  hundred  yards. 
A burning  missile  (falerica)  was  also  hurled.  The  big  ballista, 
or  siege  piece,  threw  stones  four  hundred  to  six  hundred  paces 
much  in  the  manner  of  a mortar,  and  the  onager  or  small 
ballista  was  used  as  a field  piece.  The  smaller  types  of  the 
Scorpio  and  onager  were  designed  to  be  operated  by  one  man. 

From  the  foregoing  discussion  it  is  readily  seen  how  the 
name  “Ballistics”  has  been  derived.  Now  let  us  see  how  from 
the  art  the  science  has  been  evolved. 

Following  upon  the  development  of  the  catapult  and  bal- 
lista as  machines  of  war  came  an  artillery  in  which  the  power 
for  trajection  was  supplied  by  explosives.  References  to 
explosive  substances  like  gunpowder,  or  to  burning  substances 
like  Greek  fire,  are  to  be  found  in  works  literally  as  old  as 
Moses.  Among  later  references,  some  of  the  Brahmins  of 
Alexander’s  time  are  said  by  Philostratus  to  have  been  able 
to  “overthrow  their  enemies  with  tempests  and  thunderbolts 
shot  from  their  walls”;  Archimedes,  at  Syracuse,  is  said  by 
Plutarch  to  have  “cast  huge  stones  from  his  machines  with  a 
great  noise”;  Caligula  is  stated  by  Dion  Cassius  to  have  had 
machines  which  “imitated  thunder  and  hghtning  and  emitted 
stones”;  and  Marcus  Graccus  in  the  eighth  centmy  gives  a 
recipe  of  one  pound  of  sulphur,  two  of  willow  charcoal  and  six 
of  saltpeter,  for  the  discharge  of  what  we  should  call  a rocket. 

The  use  of  Greek  fire  was  understood  as  early  as  the  sixth 
century,  but  powder  was  earliest  used  in  China,  perhaps  a 
thousand  years  before  Christ,  and  was  introduced  to  European 
notice  by  the  Saracens.  Neither  Schwartz  nor  Bacon  can  be 


104 


GUNNERY 


said  to  be  its  inventor.  Early  in  the  fourteenth  century 
cannon  and  gunpowder  appear  to  have  been  known  in  Florence; 
in  1338  mention  is  made  of  them  among  the  stores  in  the  Tower 
of  London  and  the  arsenal  at  Rouen;  and  in  1346  guns — per- 
haps hand-guns — are  said  to  have  been  used  at  Crecy. 

It  is  certain  that  the  Spanish  Moors,  shortly  after  1326, 
had  made  the  use  of  gunpowder,  fire-arms  and  cannon  well 
known  in  western  Europe,  and  by  the  end  of  the  century  they 
were  the  common  property  of  all  arnfies.  At  first  the  high 
cost  precluded  their  use  except  in  sieges  and  the  defense  of 
towns;  it  was  much  later,  at  the  battle  of  Rosabeck,  in  1382, 
between  the  Dutch  and  French,  that  field  artillery  appeared. 

At  the  end  of  the  fourteenth  century  guns  were  cast  of 
bronze,  copper  and  iron,  and  called  bombardse.  Some  of 
these  were  huge  specimens,  which  consumed  large  charges  of 
powder,  and  hurled  stone  balls  of  from  one  hundred  to  one 
thousand  pounds  weight.  Mortars  appeared  in  Italy  about 
the  middle  of  the  fifteenth  century  (1450). 

The  French  first  made  use  of  field  artillery,  which  could  be 
transported  in  the  army  trains.  That  which  accompanied 
Charles  VIII  to  Italy  in  1494  was,  comparatively  speaking, 
light,  rapid  of  fire  and  well  served.  Other  nations  gradually 
fell  into  line,  and  Gustavus  made  artillery  of  reaUy  light 
caliber.  So  we  see  that  the  original  impulse  to  the  develop- 
ment of  field  artillery  came  from  the  French  just  as  in  the 
case  of  the  radical  changes  recently  inaugurated  by  Langlois. 

By  the  middle  of  the  seventeenth  century  artillery  ceased 
to  be  merely  a guild  of  cannoneers,  as  it  had  long  been,  and 
became  an  inherent  part  of  the  army.  More  intelligence  was 
devoted  to,  and  more  money  spent  on,  this  arm;  it  grew  in 
strength  and  in  importance,  and  was  markedly  improved. 
But  while  artillery  service  ceased  to  be  a trade,  it  did  not 
assume  the  dignity  of  a recognized  special  arm  except  under 
the  great  Torstenson,  who  was  to  Gustavus  what  Senarmont 
and  Drouot  were  to  Napoleon  over  a century  and  a half  later. 


BALLISTICS 


105 


Nor  was  artillery  of  any  great  utility  in  the  field  until  well 
along  in  the  eighteenth  centm-y.  Guns,  however,  in  imitation 
of  the  Swedes,  were  lightened,  particularly  so  in  France; 
powder  was  gradually  compounded  on  better  recipes;  gun- 
metal  was  improved;  paper  and  linen  cartridges  were  intro- 
duced; gun  carriages  were  provided  with  the  aiming  wedge; 
and  many  new  styles  of  guns  and  mortars  and  ammunition 
for  them  were  invented.  Science  lent  its  aid  to  practical  men, 
and  not  only  exhausted  chemical  ingenuity  in  preparing  pow- 
der and  metal,  but  mathematical  formulas  were  made  for  the 
artillerymen,  and  the  value  of  ricochet  firing  was  discovered. 
Louis  XIV  founded  several  artillery  schools,  and  the  creation 
of  arsenals  was  begun.  Finally  the  artillery  was  organized 
on  a battery  and  regimental  basis,  and  careful  rules  were 
prescribed  for  the  tactics  of  the  guns.  These  were  served  by 
dismounted  men  and  generally  hauled  by  contract  horses. 

But  although  sensibly  improved  during  the  seventeenth 
century,  the  artillery,  in  addition  to  being  slow  of  fire,  was 
still  unskillfully  managed;  it  stood  in  small  bodies  all  along 
the  line  of  battle;  and  being  heavy  and  hard  to  move  from  one 
position  to  another,  principally  because  the  same  guns  were 
used  for  sieges  and  for  field  work,  it  was  far  from  being,  even 
relatively  to  the  other  arms,  the  weapon  which  it  is  to-day. 

Mobility  as  a prime  requisite  of  field  artillery  received 
increasing  attention  from  the  beginning  of  the  eighteenth 
century,  though  the  English,  including  Marlborough,  lagged 
far  behind  the  Continental  development.  While  Frederick 
the  Great  did  little  for  his  artillery  during  the  early  years  of 
his  career,  he  learned  by  costly  experience  a lesson  from  his 
neglect.  The  principal  defect  of  his  guns  was  their  immobility, 
in  spite  of  which  he  was  awakened  to  their  value  by  the  service 
which  they  rendered  him  in  the  battles  of  Rossbach,  Leuthen 
and  Hochkirch.  He  then  set  about  the  improvement  of  his 
artillery,  increasing  the  number  of  field  pieces  to  five  for  every 
thousand  men  of  other  arms,  also  creating  a horse-artillery 


106 


GUNNERY 


corps  of  ten  light  6-pounders,  which  was  able  to  accompany 
his  cavalry.  In  the  meantime  Austria  had  brought  her  field 
artillery  to  a higher  stage  of  development  than  Frederick. 

In  1765  Gribeauval,  for  years  called  the  “father  of  modern 
field  artillery,”  undertook  the  reconstruction  of  the  French 
system.  It  was  he  who  separated  the  artillery  into  the  classes 
now  generally  recognized,  providing  for  each  a distinct  mate- 
rial. By  decreasing  the  length  and  weight  of  the  pieces, 
omitting  ornamentation  and  strengthening  the  carriage,  de- 
creasing the  windage  and  the  charge,  he  greatly  increased  the 
mobility  of  the  system.  Gun  mechanism  and  artillery  organ- 
ization were  both  highly  developed  by  this  distinguished  ofiicer, 
but  horse  artillery  did  not  make  its  appearance  in  the  French 
army  until  1791  nor  in  the  English  army  until  1793. 

The  improvements  which  Napoleon  made  in  artillery  mate- 
rial were  not  commensurate  with  his  advance  in  the  organiza- 
tion and  tactical  employment  of  field  artillery,  the  principal 
feature  of  his  development  being  the  formation  of  divisional 
and  reserve  artillery  which  enabled  him  to  concentrate  the 
fire  of  separated  masses  of  guns.  Hitherto  the  pieces  had 
been  distributed  among  the  battalions  in  accordance  with  the 
system  of  Gustavus.  It  is  to  be  noted  that  both  Frederick 
and  Napoleon  endeavored  to  compensate  for  their  losses  by 
increasing  the  proportion  of  guns  to  infantrymen,  a fact 
indicative  of  the  value  they  attached  to  their  artillery. 

In  1803  shrapnel  was  invented  by  Major  Shrapnel  of  the 
British  service  and  Congreve  rockets  by  Sir  W.  Congreve 
soon  after.^  The  latter  were  unique  reversions  to  earlier  ar- 

^ The  derivation  of  the  name  of  the  bayonet  is  also  interesting.  It  is  said 
to  have  originated  in  Bayonne  and  was  first  used  by  General  Martinet,  the 
father  of  rigidity  and  disciphne  in  drill.  The  meaning  of  the  term  “martinet” 
is  now  clear.  The  great  exponent  of  the  bayonet,  however,  was  Suwarrow 
(Suvaroff,  Suvoroff,  Suvarov),  a Russian  field-marshal  of  Swedish  descent 
born  in  Finland  (1729-1800).  His  saying  to  the  effect  that  the  bayonet  onlj' 
has  sense  is  well  known — a saying  which  can  hardly  be  accepted  as  a sound 
maxim  in  this  day  of  long-range  fire. 


BALLISTICS 


107 


tillery  weapons,  but  seem  to  have  been  effective.  The  rocket 
consisted  of  a sheet-iron  case  inclosing  the  explosive,  and  was 
fired  from  a tube.  They  were  first  used  at  Leipzig  (1813) 
and  with  great  success;  also  in  the  Peninsular  War,  and  at 
Bladensburg  against  American  troops.  Improvement  in  the 
mobihty  of  the  British  artillery  continued  up  to  the  time  of 
the  Crimean  War.  Howitzers  were  in  general  use  among  the 
European  armies. 

While  there  is  authority  to  the  effect  that  rifling  and  breech- 
loading had  been  experimented  with  as  early  as  1547  in  Eng- 
land, it  was  not  until  the  Itahan  War  of  1859  that  rifled  field 
guns  appeared  on  the  battlefield,  being  one  of  the  many 
improvements  made  practical  by  the  French.  A breech- 
loading rifled  gun  was  first  used  by  the  British  in  the  China 
campaign  the  following  year. 

By  rifling,  the  effective  range  of  the  French  piece  was  in- 
creased to  about  2,500  yards,  the  old  smooth-bore  with  an 
effective  range  of  not  over  a mile  being  at  a great  disadvantage 
when  opposed  thereto. 

From  this  time  until  the  Franco-German  War  (1870)  little 
improvement  was  made  in  the  efficiency  of  field  guns.  During 
the  American  Civil  War  the  12-pounder  (smooth-bore)  Napo- 
leon gun  was  extensively  used,  its  effective  range  being  about 
1,500  yards.  A more  accurate  and  effective  gun  was  the  3-inch 
rifle  of  the  U.  S.  Ordnance  Department  with  a range  of  2,800 
yards.  This  war  did  far  more  for  tactics  than  material.  It 
developed  the  use  of  masses  of  guns  to  an  extent  unknown 
since  the  days  of  Napoleon  and  developed  an  audacity  in  the 
gunner  which  foreshadowed  the  Prussian  tactics  of  1870. 

After  the  Austro-Prussian  War  of  1866,  when  it  was  evident 
that  a conflict  with  France  was  at  hand,  the  Prussians  made 
vast  strides  in  the  development  of  their  artillery.  The  guns 
employed  by  them  in  the  war  of  1870  were  steel  breech-loading 
rifles.  The  French  still  used  a muzzle-loading  rifle,  though 
they  introduced  a machine  gun  known  as  the  mitrailleuse, 


108 


GUNNERY 


which  did  not  meet  the  high  expectations  it  at  first  aroused. 
The  moral  effect  of  this  new  weapon  was  very  great,  however, 
and  in  the  defense  of  positions  against  infantry  it  was  very 
effective.  It  was  a mistake,  of  course,  to  pit  them  against 
the  German  field  pieces. 

In  the  contest  for  military  superiority  among  the  great 
powers  of  the  world,  the  greatest  activity,  the  heaviest  expense, 
and  the  largest  number  of  experiments  are  now  in  the  direction 
of  the  development  of  field  artillery.  The  twenty  years  suc- 
ceeding the  Franco-German  War  saw  practically  no  trans- 
formations of  field-artillery  material.  At  the  end  of  these  two 
decades  the  usual  method  of  correcting  defects  by  remodeling 
old  types  had  become  impracticable.  The  years  1890-92 
marked  the  end  of  the  old  systems,  and  the  beginning  of  experi- 
ments culminating  in  a general  rearmament,  which  in  1910 
was  as  shown  in  the  table  of  field  guns  included  in  the  introduc- 
tory part  of  this  book. 

The  result  of  this  rivalry  of  nations,  then,  is  the  present 
rapid-fire  field  gun,  a single  one  of  which  vdU  deliver  more 
aimed  shots  in  a minute  than  a whole  battery  of  old  guns. 

It  is  not  intended  to  treat  of  material  further,  and  the 
foregoing  brief  outline  of  its  development  has  been  given 
simply  because  increased  efficiency  in  material  means  an 
advance  in  the  science  of  ballistics,  which  subject  we  are  about 
to  investigate. 

The  subject  of  ballistics  is  generally  treated  under  three 
heads — interior  ballistics,  exterior  ballistics,  and  ballistics 
of  penetration.  The  ancients,  of  course,  knew  nothing  of  the 
first,  and  little  more  of  the  third  kind  of  ballistics,  but  the 
general  laws  of  exterior  ballistics,  which  have  not  been  affected 
by  the  improved  machinery  of  modern  times,  were  somewhat 
familiar  to  them. 


CHAPTER  II 


INTERIOR  BALLISTICS 

Scope. — Interior  ballistics  is  concerned  with  the  motion 
of  the  projectile  while  in  the  bore  of  the  gun,  and  includes 
a study  of  the  conditions  existing  in  the  bore  from  the  moment 
of  ignition  of  the  powder  charge  to  the  moment  that  the 
projectile  leaves  the  muzzle. 

Practical  Results. — The  circumstances  attending  the  com- 
bustion of  the  powder,  the  pressures  exerted  by  the  gases  at 
different  points  of  the  bore,  and  the  velocities  impressed  upon 
the  projectile,  all  of  which  may  be  demonstrated  mathemati- 
cally, are  subjects  belonging  to  the  study  of  Interior  Ballistics. 

The  practical  results  of  the  study  lie  in  the  application 
of  the  deduced  formulae  which  connect  the  flight  and  the 
course  of  the  projectile  with  the  velocities  and  pressures. 
By  means  of  the  formulae  we  may  determine  the  stresses 
to  which  a gun  is  subjected  by  the  pressure  of  the  powder 
gases,  and  the  dimensions  of  the  chamber  and  bore,  and  the 
weight  of  the  powder  necessary  to  produce  in  a projectile  a 
desired  velocity.  The  action  of  different  powders  may  be  com- 
pared and  the  most  suitable  powder  selected  for  a particular 
gun.  The  interior  pressures  at  all  points  along  the  bore 
being  made  known,  the  thickness  required  in  the  walls  of 
the  gun  to  safely  withstand  these  pressures  is  determined 
from  the  principles  of  the  gun  construction.  And  so  we  see 
that  the  amount  of  powder  employed,  the  velocity  of  a pro- 
jectile, the  shape  and  dimensions  of  a gun  are  not  merely 
accidental,  but  are  based  upon  a series  of  exact  investigations, 
all  of  which  are  within  the  scope  of  Interior  Ballistics. 

109 


no 


GUNNERY 


Action  of  Powder  in  the  Gun. — Explosives,  as  we  have 
seen,  are  substances  which,  under  the  influence  of  some 
disturbing  agency,  enter  into  a chemical  reaction  accompanied 
by  the  production  of  gases  and  the  evolution  of  much  heat. 
The  powder  used  as  a charge  for  the  gun  possesses  a certain 
potential  force  or  latent  power.  Upon  combustion  the  poten- 
tial force  of  the  explosive  becomes  a kinetic  or  moving  force, 
which  is  made  use  of  for  the  purpose  of  projecting  the  missile 
through  the  air. 

The  effects  of  the  explosion  of  the  powder  upon  the  pro- 
jectile and  the  gun  are  dependent  on  the  quantity  of  gas 
evolved,  on  the  accompanying  heat,  and  on  the  rapidity  of 
the  reaction.  It  is  readily  understood  that  the  greater  the 
volume  of  gas  evolved  at  the  temperature  of  explosion,  the 
greater  the  pressure  exerted  on  the  bore  of  the  gun.  The 
rate  of  evolution  of  the  gas  of  gunpowder  is  known  as 
the  velocity  of  emission. 

The  pressure  per  unit  of  surface  exerted  by  the  gases 
from  unit  weight  of  the  explosive,  the  gases  occupying  unit 
volume  at  the  temperature  of  explosion,  is  called  the  force 
of  the  explosive.  The  progressive  emission  of  gas  from  gun- 
powder produces  a propelling  effect  by  causing  a gradual 
increase  of  pressure  on  the  base  of  the  projectile,  which  is 
made  use  of  instead  of  the  shock  resulting  from  a more  sudden 
conversion  or  detonation. 

Heat  and  Work. — The  quantity  of  heat  determines  the 
quantity  of  work  that  may  be  effected  by  the  explosion. 
The  projection  of  the  missile  from  the  gun  is  the  effect  pro- 
duced by  the  conversion  of  the  heat  of  the  explosion  into 
work.  The  total  work  that  can  be  performed  by  the  gas  from 
unit  weight  of  the  explosive  under  indefinite  adiabatic  expan- 
sion measures  the  potential  of  the  explosive. 

Adiabatic  Expansion.— By  adiabatic  expansion  is  meant 
an  expansion  of  the  gas  in  such  a manner  that  it  performs 
work  without  giving  heat  or  receiving  it.  In  this  case,  the 


INTERIOR  BALLISTICS 


111 


heat  in  the  gas  is  converted  into  work,  the  temperature  of 
the  gas  diminishing. 

In  order  to  understand  the  great  propelling  power  of  an 
explosive,  due  to  the  expansion  of  the  gas,  some  idea  of  the 
working  power  of  heat,  which  is  the  cause  of  the  expansion 
of  the  gas,  must  be  had. 

The  working  power  of  heat  or  its  mechanical  value  is 
measured  in  thermal  units.  A thermal  unit  is  the  heat  required 
to  raise  a pound  of  water  at  the  freezing-point  one  degree  in 
temperature.  The  mechanical  equivalent  of  heat  is  the 
work  equivalent  of  a thermal  unit;  that  is,  it  is  the  work 
that  can  be  performed  by  the  amount  of  heat  required  to 
raise  a pound  of  water  at  the  freezing-point  one  degree.  For 
the  Fahrenheit  scale  the  M.  E.  is  778  foot-pounds;  and  for 
the  Centigrade  scale  1,400.4  foot-pounds.  In  other  words, 
the  heat  which  will  raise  the  temperature  of  one  pound  of 
water  one  degree  Fahrenheit  wiU  move  one  pound  778  feet 
or  778  pounds  one  foot;  and  the  heat  which  will  raise  the 
temperature  of  one  pound  of  water  one  degree  Centigrade 
will  move  one  pound  1,400.4  feet  or  1,400.4  pounds  one  foot. 
This  gives  us  some  idea  then  of  the  value  of  gunpowder  as 
the  means  of  producing  heat. 

That  which  actually  occurs  when  powder  is  ignited  is 
as  follows:  In  the  first  place,  the  powder  is  converted  into 
a volume  of  gas  greater  than  that  of  the  powder;  in  the  second 
place,  the  heat  generated  by  the  explosion  expands  the  volume 
of  this  gas,  and  increases  its  pressure.  The  pressure  of  the 
gas  is  equal  in  all  directions.  Unless  the  gun  breaks,  the  expan- 
sion will  naturally  follow  the  line  of  least  resistance,  which 
is  along  the  bore.  The  pressure  due  to  the  expansion  in  this 
direction  expels  the  projectile. 

Density  of  powder  is  the  ratio  of  the  weight  of  a given 
volume  of  powder  to  the  weight  of  an  equal  volume  of  water. 
In  determining  density  the  volume  considered  is  the  volume 
actually  occupied  by  solid  powder. 


112 


GUNNERY 


Gravimetric  density  of  powder  is  the  mean  density  of 
the  contents  of  the  volume  that  is  exactly  filled  by  the  powder 
charge.  The  air  spaces  between  the  grains  are  considered 
as  well  as  the  solid  powder  in  the  charge.  The  gravimetric 
density  is  obtained  by  dividing  the  weight  of  the  charge 
by  the  weight  of  water  that  will  fill  the  volume  occupied  by 
the  charge.  It  is  evident  that,  if  a solid  block  of  powder  of 
a given  density  be  broken  up  into  grains,  the  volume  occu- 
pied by  the  powder  will  increase  and  will  be  dependent  on  the 
form  and  size  of  the  grains.  While  the  actual  density  of  the 
solid  powder  does  not  change,  the  gravimetric  density  vdll 
depend  upon  the  granulation. 

The  Gim. — The  gun  serves  two  purposes;  first,  as  the 
containing  vessel  for  the  explosive,  and  a means  of  confining 
the  gases  in  such  a way  that  the  pressure  of  expansion  will 
be  exerted  upon  the  base  of  the  projectile;  and,  second,  to 
give  the  projectile  the  proper  direction. 

So  long  as  the  gas  continues  to  exert  a forward  pressure 
upon  the  base  of  the  projectile,  it  continues  to  accelerate 
the  motion  of  the  projectile,  the  velocity  of  which  increases 
until  it  passes  out  of  the  muzzle,  and  the  pressure  on  its 
base  ceases. 

Capacity  of  Gim. — The  powder  for  a gun  of  any  caliber 
and  length  has  the  greatest  efficiency  when  in  grains  of  such 
shape  and  dimensions  that  the  charge  of  least  weight  pro- 
duces the  desired  muzzle  velocity  within  the  allowed  maximum 
pressure.  The  powder  that  produces  these  effects  may  be 
considered  the  standard  powder  for  the  gun. 

The  maximum  pressure  is  dependent  on  the  initial  sur- 
face of  the  powder  charge.  A powder  with  greater  initial 
surface  than  the  standard  powder,  that  is,  a powder  of  smaller 
granulation,  will  produce  a greater  maximum  pressure  and 
therefore  will  be  a quick  powder  for  the  gun,  and  a powder 
of  larger  granulation  will  be  a slow  powder. 

We  would  get  the  greatest  possible  effect  out  of  a charge 


INTERIOR  BALLISTICS 


113 


of  powder  if  the  gun  were  made  long  enough  to  contain  the 
whole  of  the  powder  gases,  so  that  the  forward  pressure  on 
the  base  of  the  projectile  would  cease  just  as  the  shell  reached 
the  muzzle.  Such  a gun  would,  however,  be  unwieldy,  and  in 
practice  we  cut  the  gun  short  and  allow  a good  deal  of  the 
gas  pressme  to  go  to  waste  out  of  the  muzzle.  It  is  readily  seen 
with  how  much  greater  force  the  missile  would  be  thrown 
if  the  waste  pressure  could  be  brought  to  bear  upon  it  in  addi- 
tion to  that  which  is  actually  employed. 

Length  of  Gun. — The  length  of  a gun  is  expressed  by  the 
number  of  cahbers  in  its  total  length.  Modern  rapid-fire 
field  guns  are  from  27  to  35  calibers  long.  A caliber  is  the 
diameter  of  the  bore  measured  between  opposite  ribs  of  the 
rifling.  Generally  speaking,  the  bore  is  measured  from  the 
face  of  the  breech-block  to  the  muzzle. 

Chamber  of  Gim. — The  bore  of  a gun  is  divided,  for  the 
purpose  of  internal  ballistics  only,  into  two  parts,  the  cham- 
ber and  the  bore  proper.  The  powder  does  not  completely 
fill  the  chamber,  nor  is  it  a solid  mass,  but  it  is  in  granulated 
form.  If  the  powder  charge  in  a 3-inch  shell  were  compressed 
into  a solid  block,  it  would  be  found  to  fill  a small  portion 
of  the  chamber,  possibly  a third.  On  ignition  the  powder 
gases  first  fill  the  chamber.  The  higher  the  velocity  of  igni- 
tion, that  is,  the  more  rapidly  the  gas  is  evolved  from  the 
powder,  the  sooner  will  the  pressure  of  the  chamber  over- 
come the  resistance  of  the  projectile,  causing  it  to  move  up 
the  bore.  This,  in  a field  gun,  occurs  when  the  pressure 
rises  to  about  V/2  tons  to  the  square  inch.  Henceforward 
the  pressure  of  the  gas  acts  as  an  accelerating  force  upon  the 
projectile  until  the  latter  leaves  the  muzzle. 

Effects  of  Powder  on  Design  of  Gun. — In  the  design  of 
a gun,  the  caliber,  weight  of  projectile,  and  muzzle  velocity 
being  fixed,  consideration  must  be  given  to  the  powder  in 
order  that  the  size  of  chamber,  length  of  gun,  and  thickness 
of  walls  throughout  the  length  may  be  determined.  To 


114 


GUNNERY 


produce  a given  velocity  in  a gun  a larger  charge  of  powder 
that  is  slow  for  the  gun  is  required  than  is  of  a powder  that 
is  quicker.  The  larger  charge  requires  a larger  chamber 
space,  and  thus  increases  the  diameter  of  the  gun  over  the 
chamber.  The  maximum  pressure  being  less  than  with  the 
quicker  powder,  the  walls  of  the  chamber  may  contain  less 
metal.  The  slow  powder  will  give  higher  pressure  along  the 
chase,  therefore  the  walls  of  the  gun  must  here  be  thicker, 
the  weight  of  the  gun  being  increased  throughout  its  length. 

If  we  do  not  wish  to  increase  the  diameter  of  the  chamber 
we  must,  for  slow  powder,  lengthen  the  gun  in  order  to  get 
the  desired  velocity.  On  the  other  hand,  with  a powder  that 
is  too  quick  for  the  gun  very  high  and  dangerous  pressures 
are  encountered,  requiring  excessive  thickness  of  the  walls 
over  the  powder  chamber.  The  gun  in  this  case  may  be 
thinner  walled  along  the  chase. 

It  is  evident  from  the  foregoing  considerations  that  each 
gun  must  be  designed  with  a particular  powder  in  view,  and 
that  a gun  so  designed  and  constructed  will  not  be  as  efficient 
with  any  other  powder. 

Now  let  us  follow  the  evolution  of  gunpowder  and  the 
consequent  changes  in  the  design  of  the  guns. 

Forty  years  ago  the  only  explosive  used  in  guns  was 
coarse  black  powder.  The  whole  of  the  charge  was  converted 
into  gas  almost  immediately  upon  ignition,  thus  developing 
a very  high  pressure  in  the  powder-chamber  upon  ignition, 
which  rapidly  fell  as  the  shell  moved  up  the  bore.  Guns  of 
this  period  were,  therefore,  made  of  a very  pronounced  bottle 
shape,  enormously  thick  at  the  breech.  The  old-time  field- 
piece  was,  of  course,  lighter  in  metal,  because  the  powder 
charge,  and  therefore  the  pressure,  was  comparatively  small; 
but  the  general  shape  was  much  the  same  as  that  of  the  guns 
used  in  permanent  works  and  water-batteries.  As  an  improve- 
ment on  the  old  form  of  black  powder,  pebble  powder,  in  the 
form  of  cubical  grains  of  from  one-half  inch  to  one  and  one- 


INTERIOR  BALLISTICS 


113 


half  inches,  was  introduced.  It  was  found  that  the  cubes 
burned  more  slowly  than  the  grains,  and,  since  the  gas  was 
evolved  more  slowly,  a smaller  initial  pressure  resulted,  and 
a better  maintained  pressure  as  the  projectile  moved  up  the 
bore.  Guns  were  then  made  thinner  at  the  breech  and  thicker 
at  the  muzzle. 

Prismatic  powder,  pressed  into  large  six-sided  prisms,  was 
the  next  step;  this  was  followed  by  slow-burning  brown 
powder,  known  as  cocoa  powder.  Now  we  have  smokeless 
powder,  in  thick  cords,  tubes  or  tapes,  for  long  guns,  and 


fine  strings  for  short  ones.  This  has  enabled  us  to  adjust 
the  pressures  in  the  bore  so  as  to  get  the  maximum  of  work 
out  of  the  gun  with  the  minimum  of  metal.  It  is  to  be 
observed  that  to-day  there  is  shght  difierence  in  the  metal 
at  the  breech  and  at  the  muzzle. 

A simple  and  convenient  means  of  showing  graphically  the 
pressure  in  any  gun  is  by  the  use  of  pressure  curves. 

Figure  1 gives  the  curve  for  a certain  12-inch  gun  of  old 
type  when  black  powder  was  used. 


116 


GUNNERY 


Here  the  height  of  the  curve  represents  the  pressure  in 
tons  at  that  particular  point  in  the  bore.  We  note  how  the 
pressure  rises  from  zero  to  24  tons  per  square  inch  before  the 
shell  begins  to  move,  and  runs  up  to  25  tons  before  the  shell 
has  traveled  half  of  its  length.  The  pressure  then  rapidly 
falls,  as  the  stopper,  so  to  speak,  is  drawn  out,  till  at  the  muz- 
zle it  is  only  3 tons  per  square  inch. 

As  a contrast  to  that  of  the  old  12-inch  gun,  the  curve 


for  a modern  6-inch  gun  is  shown.  The  pressure  nowhere 
exceeds  15  tons  per  square  inch  and  diminishes  gradually 
toward  the  muzzle.  We  may  also  note  how  in  both  cases 
the  pressure  curve  corresponds  in  a general  way  to  the  pro- 
file of  the  guns.  This  is,  as  has  been  shown,  because  the  gun 
was  cast  or  constructed  to  withstand  the  pressure  to  which 
it  would  be  subjected,  its  shape  not  being  merely  accidental. 


CHAPTER  III 


EXTERIOR  BALLISTICS 

Exterior  ballistics  treats  of  the  motion  of  a projectile  after 
it  has  left  the  piece. 

We  have  already  seen  that  the  trajectory  is  the  course 
of  the  projectile  during  its  flight.  To  be  mathematically 
exact,  it  is  the  curve  GMT,  described  by  the  center  of  gravity 
of  the  projectile  during  its  passage  through  the  air. 

Every  trajectory  is  theoretically  an  analytical  curve. 
That  is,  it  is  such  a curve  that  it  may  be  analyzed  with  respect 
to  its  ordinates.  In  other  words,  the  horizontal  distance  of  any 
point  on  the  curve  bears  a definite  and  fixed  relation  to  the 
vertical  distance  of  that  point,  from  another  given  point. 


Thus  in  Figure  1,  the  horizontal  ordinate  x,  of  the  point 
M,  bears  a definite  relation  to  the  vertical  ordinate  y,  and 
given  certain  other  factors,  such  as  the  resistance  of  the  air, 
the  velocity  of  the  projectile,  etc.,  etc.,  knowing  the  value 
of  either  ordinate,  the  other  may  be  determined. 

117 


118 


GUNNERY 


While  a certain  motion  of  the  projectile  to  be  hereinafter 
considered  effects  the  trajectory,  the  curve  ordinarily  con- 
sidered is  the  projection  of  the  actual  curve  upon  the  vertical 
plane  of  fire.  This  projection  so  nearly  agrees  with  the  actual 
trajectory  that  the  results  obtained  are  practically  correct. 


The  Range,  hf,  (Figure  2)  is  the  distance  from  the  muzzle 
of  the  gun  to  the  target. 

The  Line  of  Sight,  abf,  is  the  straight  line  passing  through 
the  sights  and  the  point  aimed  at. 

The  Line  of  Departure,  hC,  is  the  prolongation  of  the  axis 
of  the  bore  at  the  instant  the  projectile  leaves  the  gun. 

The  Line  of  Fire,  6K,  is  the  prolongation  of  the  axis  of 
the  bore  before  the  projectile  leaves  the  piece. 

Jump. — When  the  piece  is  discharged  the  muzzle  of  the 
piece  jumps  upward,  while  the  projectile  is  mo\ung  through 
the  bore.  The  movement  of  the  axis  is  due  to  the  elasticity 
of  the  parts  of  the  carriage,  to  the  play  in  the  trunnion  beds 
and  between  the  parts  of  the  carriage,  and  in  some  cases  to 
the  action  of  the  elevating  device  as  the  gun  recoils.  The  jump 
must  be  determined  by  experiment  for  the  indi\ddual  piece 
in  its  particular  mounting,  and  for  the  projectile  and  the  pow- 
der charge  used.  Jump  increases  the  angle  of  elevation,  so 
that  the  angle  of  departure  is  greater  than  the  former.  It 
is  measured,  therefore,  by  the  angle  J,  or  the  angle  between 
the  line  of  fire  and  the  line  of  departure. 

The  Plane  of  Fire  or  Plane  of  Departure  is  the  vertical 
plane  through  the  line  of  fire  or  through  the  line  of  departure. 


EXTERIOR  BALLISTICS 


119 


The  Angle  of  Position  or  Angle  of  Sight,  e,  is  the  angle 
made  by  the  line  of  sight  with  the  horizontal.  This  angle 
is  referred  to  as  the  Angle  of  Site  in  Practical  Gunnery. 

The  Angle  of  Departure,  C,  is  the  angle  made  by  the  line 
of  departure  with  the  line  of  sight. 

The  Quadrant  Angle  of  Departure,  C + is  the  angle  made 
by  the  line  of  departure  with  the  horizontal. 

The  Angle  of  Elevation,  C',  is  the  angle  between  the  line 
of  sight  and  the  line  of  fire,  or  with  the  axis  of  the  piece  when 
the  gun  is  aimed. 

The  Point  of  Fall,  or  Point  of  Impact,  f,  is  the  point  at 
which  the  projectile  strikes. 

The  Angle  of  Fall,  W,  is  the  angle  made  by  the  tangent  to 
the  trajectory  with  the  line  of  sight  at  the  point  of  fall. 

The  Striking  Angle,  W',  is  the  angle  made  by  the  tangent 
to  the  trajectory  with  the  horizontal  at  the  point  of  fall. 

Velocity  is  the  rate  of  motion  or  the  rate  at  which  a body 
changes  its  position  in  space.  It  is  measured  in  feet  per 
second. 

Initial  Velocity  is  the  velocity  of  the  projectile  at  the 
muzzle.  It  is  sometimes  spoken  of  as  muzzle  velocity. 

Remaining  Velocity  is  the  velocity  at  any  point  of  the  trajec- 
tory intermediate  between  the  muzzle  and  the  point  of  impact. 

Final  Velocity  is  the  velocity  at  the  end  of  the  range. 

Fire  Classified  as  to  Angle  of  Elevation. — Direct  Fire  is 
from  guns  with  service  charges  at  all  angles  of  elevation  not 
exceeding  15°. 

Indirect  or  Curved  Fire  is  from  guns  with  less  than  service 
charges,  and  from  howitzers  and  mortars,  at  all  angles  not 
exceeding  15°. 

High- Angle  Fire  is  from  guns,  howitzers,  and  mortars,  at 
any  angle  exceeding  15°. 

Fire  Classified  as  to  Direction. — Front  or  Frontal  Fire  is 
that  which  is  directed  perpendicularly,  or  nearly  so,  to  the 
front  of  the  target. 


120 


GUNNERY 


Oblique  Fire  is  that  which  is  directed  obhquely  to  the  front 
of  the  target.  Frontal  fire  penetrates  the  target  at  one  point. 


Oblique  fire  not  only  penetrates  the  target,  but  renders  a 
greater  space  in  advance  thereof  untenable. 

Enfilade  or  Raking  Fire  is  that  which  rakes  a target,  the  gun 
from  which  it  is  delivered  being  on  a flank  of  the  target.  It  is 
naturally  the  most  destructive  and  demoralizing  form  of  fire. 

Flanking  Fire  is  one  directed  along  the  front  of,  or  nearly 
parallel  to,  the  line  to  be  flanked  or  defended.  The  term  has 
respect  to  the  position  of  the  troops  to  which  the  gun  belongs. 

Reverse  Fire  is  fire  delivered  upon  the  target  by  a gun 
in  rear  thereof. 

Cross-Fire  is  where  projectiles  from  guns  in  different 
positions  cross  one  another  at  a particular  point  of  ground. 

The  Unimpeded  Motion  of  a Projectile. — Suppose  a shell 
be  fired  in  vacuo  in  a horizontal  direction  with  a velocity 
of  1,000  feet  per  second.  Then  its  path  will  be  determined 


EXTERIOR  BALLISTICS 


121 


by  the  two  forces  acting  on  it,  namely,  the  impetus  of  the  shell, 
which  tends  to  carry  it  forward  in  the  direction  in  which  it 
started;  and  the  force  of  gravity,  which  tends  to  pull  it  down 
to  the  earth. 


4000 


We  know  that  a falling  body  drops  (neglecting  decimals), 
or 

16  X 1^  = 16  feet  by  the  end  of  the  first  second 
16  X 22  = 64  ‘‘  “ “ “ second  “ 

16  X 32  = 144  ‘‘  “ “ “ ''  third 

16  X 42  = 256  “ “ “ fourth  “ 

16  X 52  = 400  “ “ “ “ ‘‘  fifth 

and  so  on. 

Then  by  the  end  of  the  first  second  the  shell  will  have 
traveled  1,000  feet  forward  and  have  dropped  16  feet  down- 
ward, so  that  its  position  will  be  at  A. 

At  the  end  of  the  next  second  it  will  have  traveled  another 
1,000  feet  forward,  and  will  have  dropped  altogether  64  feet, 
and  its  position  will  be  at  B;  and  so  on. 

If  the  shell  be  fired  in  a vacuum,  as  is  imagined  in  the 
preceding  paragraphs,  the  curve  of  the  trajectory  would  be 
a parabola.  But  in  practice,  as  will  be  explained  hereafter, 
the  shape  of  the  trajectory  is  considerably  modified  by  the 
resistance  of  the  air. 

Shell  Fired  Vertically. — If  a shell  be  fired  straight  up 
into  the  air,  at  a velocity  of  1,000  feet  per  second,  it  will 


122 


GUNNERY 


continue  to  fly  upward  until  the  ever-increasing  downward 
velocity,  due  to  gravity,  exceeds  1,000  feet  per  second,  when 
it  will  begin  to  fall. 

To  v/ork  this  out  practically  we  must  use  the  formula: 

V = gt. 

Here  V is  the  velocity,  g the  acceleration  due  to  gravity, 
and  t the  time  in  seconds.  Now  g is  always  the  same,  since 
the  force  of  gravity  does  not  vary,  and  is  equal  to  32  feet 
(strictly  32.2  feet)  per  second. 

Some  confusion  may  arise  in  the  student’s  mind  between 
the  32  feet  of  acceleration  due  to  gravity,  and  the  16  feet 
through  which  the  body  drops  in  the  first  second. 

Now  if  a body  falls  from  rest,  it  falls  faster  and  faster, 
until  at  the  end  of  the  first  second  it  is  traveling  at  the  rate 
of  32  feet  per  second.  This  acceleration  of  velocity  from  0 
to  32  feet  per  second  is  “g,”  and  every  unsupported  body 
gets  an  extra  velocity  of  32  feet  imparted  to  it  by  gra\dty 
every  second.  If  the  body  be  supported,  then  the  effect  of 
gravity  is  to  cause  a continuous  stress  on  the  support. 

It  will  be  apparent  on  consideration  that  the  distance 
through  which  a body  falls  in  the  first  second  is  not  32  feet, 
since  the  body  only  attains  that  velocity  at  the  end  of  the 
second.  The  distance  corresponds  to  the  mean  velocity  of 
the  body  during  that  second,  which  is  half-W’ay  between  0 
and  32,  or  16  feet 

To  return  to  the  question  of  the  shell  fired  vertically 
upward.  As  we  have  stated,  V = gt,  that  is,  for  every 
second  that  the  shell  is  in  the  air  it  acquires  an  increasing 
downward  velocity  of  32  feet.  At  the  end  of  10  seconds  it 
will  have  acquired  320  feet  per  second  dovmward  velocitj^; 
but  since  its  impetus  continues  to  drive  it  upward  at  1,000 
feet  per  second,  its  actual  remaining  upward  velocity  will 
be  680  feet  per  second. 

At  the  end  of  30  seconds  its  downward  velocity  will  be 


EXTERIOR  BALLISTICS 


123 


960  feet,  and  at  the  end  of  32  seconds  1,024  feet;  so  that  at 
some  time  in  the  32d  second  (actually  at  3134  seconds)  the 
upward  velocity  will  balance  the  downward  velocity,  and  the 
shell  will  begin  to  fall  again.  Thenceforward,  the  velocity 
will  increase  at  the  rate  of  32  feet  per  second  until  the  shell 
reaches  the  earth  again. 

Its  velocity  on  reaching  the  earth  will  be  31)4  multiplied 
by  32,  or  1,000  feet  per  second,  which  we  see  is  equal  to  that 
with  which  it  started. 

Elevation. — Since  the  shell  is  falling  during  the  whole 
time  of  flight,  then  in  order  to  reach  the  target  it  must  be 
directed  at  a point  above  the  target.  The  height  of  this 
point  must  be  equal  to  the  distance  through  which  the  shell 
falls  during  the  time  of  flight.  (See  Figure  5.) 


Thus  if  the  shell  be  fired  at  an  object  3,000  feet  distant 
with  a velocity  of  1,000  feet  per  second,  it  will  take  3 seconds 
to  reach  the  target.  And  since  in  3 seconds  the  shell  will 
fall  16  X 3^  = 144  feet,  therefore  it  must  be  directed  at  a 
point  144  feet  above  the  target. 

Since  the  parabola  which  a shell  describes  in  vacuo  is  a 
regular  curve,  with  its  ascending  and  descending  branches 
alike,  the  greatest  height  attained  by  the  shell  will  be  at  a 
point  half-way  between  the  range. 

For  simplicity,  we  will  take  the  case  of  a shell  with  a M. 
V.  of  1,000  feet  and  a time  of  flight  of  4 seconds.  The  point 
at  which  the  shell  is  aimed  will  be  16  x 4^  = 256  feet  above 
the  target,  and  point  C in  the  center  of  the  range  will  be  128 
feet  high.  Half-way  down  the  range  the  shell  will  have  been 


124 


GUNNERY 


falling  two  seconds,  and  will  be  64  feet  below  C,  or  128  — 64 
= 64.  This  is  one-quarter  of  the  height  of  A,  and  this  propo- 
sition holds  good  for  any  shell  describing  a parabola. 

Since  the  height  of  A in  feet  is  sixteen  times  the  square 


of  the  time  of  flight,  therefore  the  greatest  height  attained 
by  the  shell  is  four  times  the  square  of  the  time  of  flight,  or 

H = 4T2. 

This  formula  is  given  here  because  it  is  practically  useful. 
At  medium  ranges  the  first  half  of  the  trajectory  of  a field  gun 
fired  under  ordinary  conditions  is  not  very  different  from 
a parabola,  and  the  formula  is  sufficiently  near  the  truth  for 
practical  purposes.  The  time  of  flight  is  always  knovui  either 
from  the  range  table  or  the  fuse  scale,  and  this  gives  us  a 
ready  means  of  determining  the  height  of  the  trajectory. 

The  Rigidity  of  the  Trajectory. — According  to  the  princi- 
ple of  the  rigidity  of  the  trajectory,  which  may  be  mathe- 
matically demonstrated,  the  relations  existing  between  the 
curve  and  the  chord  representing  the  range  are  practically 
the  same  for  direct  fire,  whether  the  chord  be  horizontal  or 
at  an  angle  to  the  horizontal.  In  other  words,  the  curve  is 
practically  the  same  whether  the  target  be  on  the  same  level 
with  the  piece,  or  above  or  below  it. 

Thus,  if  the  ranges  GT  and  GT'  (Figme  7)  are  equal, 
the  curve  GOT  bears  the  same  relation  to  its  chord,  GT, 


A 


4000  yds.  - 
Fig.  6. 


EXTERIOR  BALLISTICS 


125 


that  the  curve  GO'T'  bears  to  its  chord  GT',  and  the  maxi- 
mum ordinates  at  O'  and  O are  equal. 

The  Motion  of  a Projectile  in  Air. — A projectile  traveling 
through  the  air  experiences  a certain  resistance,  which  shortens 
the  distance  of  its  flight  and  alters  the  shape  of  the  trajectory. 


This  resistance  is  greater  at  high  than  at  low  velocities,  but 
the  rate  of  increase  does  not  follow  any  simple  rule. 

Up  to  about  800  feet  per  second  it  increases  as  the  square 
of  the  velocity;  that  is,  a shell  traveling  at  300  feet  per  second 
experiences  9 times  as  much  resistance  as  one  traveling  at 
100  feet  per  second.  Above  800  fs.  the  resistance  increases  in 
a higher  ratio.  For  velocities  between  1,000  and  2,500  feet 
per  second  the  resistance  may  be  said  to  increase  roughly 
as  the  cube  of  the  velocity. 

It  will  be  readily  understood  that  the  resistance  is  in  direct 
proportion  to  the  surface  offered  to  the  air,  that  is  to  the 
cross  section  of  the  projectile.  This  is  apparent,  since  two 
projectiles  side  by  side,  each  one  square  inch  in  cross  section, 
will  experience  twice  as  much  resistance  as  one  such  projec- 
tile. 

Shape  of  Head. — The  resistance  is  affected  in  a marked 
degree  by  the  shape  of  the  head  of  the  shell.  It  is  found 
that  in  a shell  of  the  usual  form  the  shape  of  the  shoulders 
is  more  important  than  that  of  the  actual  point.  It  is  sug- 
gested as  an  explanation  of  this  that  as  the  air  streams  out- 
ward from  the  point  to  pass  over  the  shoulders  of  the  shell 
it  leaves  a partial  vacuum  in  front  of  the  point,  while  the 


126 


GUNNERY 


main  air-pressure  comes  near  the  shoulders.  But  when  a 
shell  with  an  ogive  of  5 or  6 calibers  radius  is  used,  the  shape 
of  the  point  becomes  important,  as  determining  the  stream 
lines,  or  direction  of  the  currents  of  air  which  flow  over  the 
shoulders  of  the  shell. 

Smoothness. — It  is  also  found  that  a modern  smooth  steel 
shell  with  di’iving-band  meets  with  less  resistance  than  the 
old  cast-iron  studded  shell. 

Steadiness. — If  a shell  wobbles  and  travels  shoulder  flrst, 
its  cross-section  is  naturally  larger,  and  the  resistance  it  meets 
with  greater,  than  if  it  traveled  point  first.  Modern  shell 
are  steadier  in  flight  than  those  formerly  used. 

Taper-Base  Shell. — The  ideal  shape  of  a shell  intended 
to  travel  through  the  air  with  the  minimum  of  resistance 
is  that  of  a Whitehead  torpedo,  with  a long  tapering  “tail.” 
Theoretically,  the  shape  of  the  base  is  more  important  than 
that  of  the  head — just  as,  in  ship  designing,  a fine  run  is 
found  even  more  conducive  to  speed  than  a sharp  entrance. 
The  flat  sawed-off  bottom  of  the  service  shell  is  objectionable, 
for  several  reasons.  It  forms  a partial  vacuum  behind  it, 
causing  an  unbalanced  air-pressure  on  the  head  of  the  shell, 
and  the  air  rushing  into  this  vacuum  forms  eddies  which 
tend  to  unsteady  the  shell.  It  would  therefore  appear  desir- 
able to  introduce  a more  scientific  form  of  projectile.  This 
idea  was  carried  out  successfully  in  the  original  "WTiitworth 
solid  shot,  which  was  the  first  accurate  artillery  projectile 
ever  invented.  But  modern  experiments  have  given  less 
favorable  results.  The  Zalinski  torpedo  shell,  fired  from 
an  air-gun,  had  a habit  of  pitching  in  unexpected  places. 
And  at  a trial  carried  out  in  Switzerland  in  1903  it  was  found 
that  although  the  taper-base  shell  ranged  further  than  the 
ordinary  pattern,  they  were  decidedly  inaccurate  in  flight. 
It  would,  however,  be  a mistake  to  condemn  a theoretically 
sound  design  on  the  strength  of  a single  experimental  series. 
The  failure  of  the  Swiss  experiments  only  showed  that  some- 


EXTERIOR  BALLISTICS 


127 


thing  was  wrong — probably  the  twist  of  the  rifling  was  unsuited 
to  these  particular  shell.  It  is  to  be  hoped,  therefore,  that, 
in  spite  of  the  obvious  manufacturing  difficulties,  modern 
science  may  evolve  a better  shape  than  that  of  the  cylindro- 
ogival  shell  which  forms  our  present  equipment. 

Density  of  Air. — When  the  barometer  is  high  the  air 
is  compressed  and  is  denser  than  when  it  is  low;  on  the  other 
hand,  when  the  thermometer  is  high  the  air  expands  and  is 
less  dense  than  when  the  temperature  is  low.  Since  the 
resistance  to  a projectile  is  greater  when  the  air  is  denser, 
the  pressure  and  temperatme  must  be  taken  into  account 
in  all  accurate  work,  such  as  practice  for  range  and  accuracy. 

Temperature. — Besides  the  effect  of  the  temperature  on 
the  density  of  the  air,  it  has  another  and  practically  much 
more  important  action,  namely,  its  effect  upon  the  powder. 
All  modern  smokeless  powders  are  comparatively  sensitive 
to  changes  in  temperature,  and  a rise  in  the  thermometer 
usually  means  an  increase  of  muzzle  velocity.  The  amount 
of  such  increase  varies  for  each  particular  size  and  sample 
of  powder,  and  cannot  well  be  tabulated. 

Flatness  of  Trajectory  and  Dangerous  Space. — A trajec- 
tory may  be  flat,  that  is  approaching  a straight  line,  or  eccen- 
tric, that  is  very  curved. 

The  perpendicular  let  fall  from  the  highest  point  of  the 
curve  to  the  line  of  sight  is  the  maximum  ordinate  of  the 
trajectory. 

We  have  seen  that  the  curve  of  the  trajectory  in  vacuo 
would  be  a parabola.  The  maximum  ordinate  in  such  a 
case  would  be  at  the  middle  of  the  range,  since  the  curve  is 
regular.  In  air,  however,  the  angle  of  fall  is  always  greater 
than  the  angle  of  departure,  and  hence  the  highest  point  of 
a trajectory  is  nearer  the  point  of  fall  than  the  piece.  As  the 
range  increases,  then  the  maximum  ordinate  creeps  toward 
the  target.  Oi  is  at  the  middle  of  range  GiTi,  but  O2  is  nearer 
T2  than  Gi  by  the  distance  CO2. 


128 


GUNNERY 


A shell  which  travels  high  above  the  earth  to  reach  the 
target  is  clearly  ineffective  against  an  enemy  standing  anywhere 
except  at  the  exact  point  where  the  shell  pitches.  On  the  other 
hand,  a shell  which  flies  along  comparatively  close  to  the 
ground  will  strike  a six-foot  man  standing  anywhere  between  the 


O2 


place  where  the  shell  pitches  and  the  point  where  the  trajectory 
comes  within  six  feet  of  the  ground.  This  space  over  which 
an  enemy  is  liable  to  be  struck  by  a projectile  fired  at  a given 
point  is  called  the  dangerous  zone,  and  it  is  the  object  of  the 
gun-designer  to  make  this  dangerous  zone  as  deep  as  possible; 
not  so  much  on  account  of  the  shell  as  on  account  of  the  shrap- 
nel bullets  which  issue  from  it.  This  is  secured  by  flatness 
of  trajectory — that  is,  by  projecting  the  shell  so  that  the 
height  above  the  earth  which  it  reaches  is  as  small  as  possible. 

The  dangerous  space  for  any  object  may  be  readily  deter- 
mined. Suppose  an  object  is  6 feet  high.  "Wdien  the  projec- 
tile leaves  the  piece  it  ascends  and  then  descends.  If  we 
determine  the  distance  from  the  piece  at  which  the  height 
of  the  trajectory  is  6 feet,  it  is  evident  that  for  every  point 
beyond  this  distance,  in  the  descending  branch  of  the  trajec- 
tory, the  height  will  be  less  than  6 feet,  and  the  object  wiU 
be  struck.  The  dangerous  space,  then,  is  the  difference  between 
the  whole  range  and  the  distance  to  the  point  at  which  the 
trajectory  is  6 feet  high. 

It  is  also  evident  that  in  general  there  will  be  two  points 
of  the  trajectory  whose  heights  are  the  same — one  point 
in  the  ascending,  and  one  in  the  descending  branch.  The 
latter  only  is  considered. 


EXTERIOR  BALLISTICS 


129 


It  is  evident  that  very  flat  trajectories  possess  certain 
advantages,  for  if  the  maximum  ordinate  is  less  than  the  height 
of  animate  objects  they  will  be  struck  at  any  point  of  the 
range.  The  total  range  is  then  dangerous  space  and  when 
such  is  the  case  it  is  called  the  maximum  continuous  dan- 
gerous space,  or  the  danger  range. 

An  error  in  estimating  range  is  also  of  less  importance 
with  such  a trajectory,  since  if  the  projectile  reach  the  point 
where  the  target  is  actually  situated  it  will  be  struck  even 
though  it  be  not  where  the  projectile  would  have  fallen. 

It  will  now  be  more  readily  understood  why  long  ranges, 
where  trajectories  are  high  and  have  large  angles  of  fall, 
are  less  effective  than  short  ranges,  where  the  dangerous 
space  is  greater  due  to  the  flatness  of  the  trajectories  and  the 
consequent  smallness  of  the  angles  of  fall.  The  accuracy  of 
fire  may  be  as  great  in  one  case  as  in  the  other.  At  long 
ranges,  however,  a very  limited  space  is  subjected  to  the 
fire — that  is  the  point  at  which  the  projectile  actually  falls; 
whereas  at  short  ranges  a considerable  space  in  front  of  the 
target  is  swept  while  the  projectile  is  traversing  the  dangerous 
space. 

The  advantage  of  short  ranges  with  respect  to  dangerous 


space,  and  therefore  the  effectiveness  of  the  fire,  is  illustrated 
in  the  foregoing  figure  in  which  the  horizontal  dotted  line 
is  at  the  height  of  a man’s  head  from  the  ground.  As  the 
angle  of  fall  increases  the  danger  zone  diminishes. 

The  danger  zone,  dT,  of  the  range  GT  is  seen  to  be  much 
deeper  toward  G than  is  d^T^,  and  d^T^. 

High  Velocity. — Now  we  have  seen  that  it  is  necessary 


130 


GUNNERY 


to  project  a shell  to  a certain  height  in  order  to  reach  a target 
in  a given  number  of  seconds.  And  no  human  power  can 
alter  the  height  through  which  a shell  falls  in  a given  time. 
To  obtain  a flat  trajectory,  therefore,  all  that  we  can  do 
is  to  reduce  the  time  of  flight  as  much  as  possible. 

If  the  velocity  of  a shell  is  3,000  feet  per  second,  it  would 
reach  a target  3,000  yards  distant  in  one  second,  and  the 
greatest  height,  4T^,  would  be  4 feet.  If  the  velocity  were 
1,500  fs.  the  time  of  flight  would  be  2 seconds,  and  the  greatest 
height  16  feet,  giving  a dangerous  zone  of  about  200  yards 
in  front  of  the  target.  Thus,  we  see  that  to  procure  a flat 
trajectory  and  deep  dangerous  zone  we  must  have  a high 
velocity,  enabling  us  to  use  a small  angle  of  elevation. 

Angle  of  Descent. — Flatness  of  trajectory  is  estimated  in 
practice  by  the  smallness  of  the  angle  of  descent.  The  field 
gunner’s  object  is  to  burst  his  shrapnel  so  that  the  bullets 
do  not  pitch  straight  forv^ard  into  the  ground,  but  sweep 
along  it,  so  as  to  produce  good  effect  in  spite  of  ine^dtable 
errors  of  range.  For  this  he  requires  a small  angle  of  descent, 
which  is  only  possible  with  a high  muzzle  velocity. 

Greatest  Possible  Range. — The  greatest  possible  range 
in  vacuo  is  obtained  when  the  angle  of  elevation  is  45  degrees. 
When  fired  in  air  the  angle  giving  the  greatest  range  is  not 
materially  different,  being  between  40  and  43  degrees  Little 
is  gained  by  increasing  the  angle  of  elevation  beyond  35  degrees. 

Rifling. — Rifling  is  a means  of  impartiug  rotation  to  the 
shell.  In  all  modern  guns  this  is  effected  by  cutting  helical 
grooves  down  the  bore,  leaving  raised  ribs  called  “lands” 
between  them.  A band  of  soft  copper  is  secured  round  the 
shell  near  the  base.  On  discharge  the  shell  with  its  copper 
driving-band  is  projected  up  the  bore;  the  ribs  cut  into  the 
soft  copper  and  force  the  shell  to  follow  their  helical  course 
and  to  rotate.  This  rotation  continues,  somewhat  diminished 
by  the  friction  of  the  air,  to  the  end  of  the  shell’s  flight. 

The  only  method  of  rifling  now  in  use  is  the  polygroove 


EXTERIOR  BALLISTICS 


131 


system  (so  called  from  the  large  number  of  small  grooves) 
and  the  copper  driving  band. 

Object  of  Rifling. — Any  rapidly  rotating  body  tends  to 
preserve  the  direction  of  its  axis  of  rotation — that  is,  to  keep 
in  the  same  direction  in  which  it  pointed  when  first  made  to 
rotate.  A familiar  instance  of  this  is  the  spinning  top. 

Not  only  does  a spinning  body  tend  to  preserve  the  direc- 
tion of  its  axis  of  rotation  when  left  alone,  but  it  actively 
resists  any  attempt  to  change  that  direction. 

Thus,  if  we  attempt  to  upset  a spinning  top  by  striking 
it  with  a ruler,  we  shall  find  some  difficulty  in  doing  so.  Instead 
of  overturning,  the  top  will  fly  off  sideways,  still  keeping 
vertical. 

This  property  of  rotating  bodies  is  turned  to  account 
to  make  the  shell  travel  point  flrst  during  its  flight.  But 
for  the  spin  given  to  the  shell  it  would  soon  turn  over  and 
fly  sideways  when  its  direction  would  become  erratic  and  its 
range  would  be  much  reduced. 

The  object  of  rifling  may,  then,  be  said  to  be  to  enable 
a gun  to  fire  an  elongated  projectile  with  accuracy. 

Advantages  of  Elongated  Projectiles. — Since  a shell  three 
calibers  long  has  a cross-section  only  one-third  of  that  of  a 
spherical  shell  of  the  same  weight,  it  can  be  fired  from  a much 
smaller  and  lighter  gun.  And  since  it  only  opposes  to  the 
air  a resistance  one-third  of  that  of  the  spherical  shell,  it 
ranges  much  further.  And  moreover  since  in  penetrating 
an  obstacle  it  makes  a hole  only  one-third  the  size  of  that 
made  by  a spherical  shell,  it  will  penetrate  more  readily. 

These  advantages  may  be  said  to  be  due  to  rifling,  which 
renders  it  possible  to  use  the  elongated  shell. 

Twist  of  Rifling. — A spinning  top  is  acted  on  by  its  weight, 
which  constantly  tends  to  make  it  fall  flat,  and  its  energy 
of  rotation,  which  keeps  it  vertical.  When,  owing  to  the 
friction  of  the  peg  of  the  top,  the  energy  of  rotation  is  suffi- 
ciently diminished,  the  top  overbalances. 


132 


GUNNERY 


Now,  with  a shell,  the  force  tending  to  overturn  it  is  the 
pressure  due  to  the  resistance  of  the  air,  and  that  tending 
to  keep  it  straight  is  the  rotation  due  to  the  rifling.  The 
former  tends  to  constantly  diminish  as  the  shell  expends 
its  velocity  in  overcoming  the  resistance  of  the  air;  but  the 
spin  is  affected  only  by  the  surface-friction  between  the  shell 
and  the  air,  and  reduces  it  to  a less  extent.  For  flat  trajec- 
tories, it  follows,  then,  that  if  we  give  the  shell  enough  spin 
to  keep  it  straight  at  starting,  this  will  suflace  to  keep  it  point 
foremost  to  the  end  of  its  flight. 

Minimum  Twist. — The  longer  the  shell  in  proportion  to 
its  diameter  the  greater  the  amount  of  spin  required.  It 
will  be  afterwards  seen  that  it  is  desirable  not  to  allow  an 
undue  amount,  as  this  increases  the  lateral  curvature  of  the 
path  of  the  shell. 

Uniform  and  Increasing  Twist. — It  will  be  readily  under- 
stood that  if  a heavy  shell  has  a high  velocity  of  rotation 
suddenly  forced  upon  it,  this  must  cause  a severe  strain  both 
on  the  shell  and  on  the  gun.  To  avoid  this,  the  grooves 
of  the  rifling  are  made  to  run  at  first  straight  down  the  gun, 
gradually  increasing  in  inclination  or  “pitch”  till  the  full 
velocity  of  rotation  is  attained.  This  is  known  as  an  “increas- 
ing twist,”  in  contradistinction  to  the  older  “uniform  tT\dst,” 
in  which  the  pitch  of  the  rifling  was  the  same  all  down  the 
bore. 

The  increasing  twist,  however,  has  the  advantage  of  causing 
greater  friction  in  the  bore  and  consequent  loss  of  velocity. 
For  the  indents  made  by  the  lands  in  the  driving-band  have 
to  be  forcibly  displaced  as  the  shell  travels  down  the  bore 
and  the  inclination  of  the  lands  alter. 

Position  of  the  Driving-Band. — At  first  sight  it  would 
seem  desirable  to  put  the  driving-band  as  near  the  center 
of  gravity  of  the  shell  as  possible,  but  in  practice  this  is  not 
the  case.  The  walls  are  too  thin  at  the  center  of  the  shell 
to  carry  the  driving-band.  Moreover,  the  body  of  the  shell 


EXTERIOR  BALLISTICS 


133 


can  never  be  a close  fit  in  the  bore,  and  after  the  driving-band 
had  emerged  from  the  muzzle  it  would  be  followed  by  some 
6 inches  of  ill-fitting  body,  with  the  powder-gases  escaping 
past  one  side  of  it,  which  would  unsteady  the  shell.  Accord- 
ingly the  driving-band  is  always  set  as  far  back  as  possible, 
leaving  only  sufficient  metal  behind  it  to  afford  a grip  for 
the  cartridge  case. 

Forward  Steadying  Band. — The  unsteadiness  or  oscillation 
of  the  shell  in  the  bore,  due  to  its  imperfect  fit,  is  a serious 
cause  of  inaccurate  shooting.  Attempts  have  been  made  to 
overcome  this  by  fitting  a forward  band  in  addition  to  the 
driving-band.  It  is  said  that  the  new  Austrian  field  shell 
has  a steadying  band  of  this  nature.  The  subject  is  beset  with 
difficulties.  If  an  increasing  twist  is  used,  the  forward  band 
must  on  no  account  take  the  rifling.  If  the  forward  band 
is  to  be  a good  fit  in  the  bore,  then  the  bands  must  be  eased 
at  the  breech  in  order  to  enable  the  shell  to  be  rammed  home. 
The  walls  have  to  be  thickened  at  the  shoulder  to  take  the 
band.  In  spite  of  these  difficulties,  it  would  seem  worth 
while  to  try  the  steadying  band  in  field  guns  with  uniform 
twist  of  rifling,  in  order  to  obtain  increasing  accuracy  for 
fire  at  shielded  guns. 

Drift. — The  tendency  of  a projectile  fired  from  a gun 
rifled  with  a right-hand  twist  is  to  drift  or  whirl  out  of  the 
plane  of  fire  to  the  right.  This  divergence  increases  rapidly 
with  the  range — about  as  the  square  thereof.  The  rough 
correction  of  deflection  for  drift  is  set  forth  in  paragraph 
327  Drill  Regulations  at  3 mils  up  to  3,500  yards  and  5 mils 
for  longer  ranges. 

The  subject  of  drift  is  a very  difficult  and  complicated 
one  and  we  understand  few  of  the  laws  governing  this  motion. 

Although  the  effect  of  the  resistance  of  the  air  tends  to 
keep  the  shell  pointing  in  the  direction  of  its  motion,  yet 
the  spin  of  the  shell  constantly  resists  this  tendency,  and 
tries  to  keep  the  shell  parallel  to  its  original  direction.  The 


134 


GUNNERY 


result  is  a compromise,  and  the  shell  travels  with  its  nose 
cocked  in  the  air,  well  above  the  line  of  the  trajectory. 

Now  if  we  remember  that  the  shell,  viewed  from  behind, 
is  spinning  in  the  direction  of  the  hands  of  a clock,  then  it 
will  be  evident  that  its  friction  against  the  air  resistance, 
which  takes  it  below  the  center,  must  tend  to  make  the  shell 
gradually  deviate  to  the  right.  And  since  the  spin  of  the  shell 
diminishes  more  slowly  than  the  forward  velocity,  therefore 
the  path  of  the  shell  curves  more  and  more  to  the  right. 

Thus  if  we  suppose  that  the  spin  of  the  shell  carries  it 
ten  feet  to  the  right  every  second,  then  in  the  first  second  the 
shell  will  travel  say  1,500  feet  forward  and  10  feet  sideways, 
and  will  have  acquired  a side  velocity,  at  right  angles  to 
the  line  of  fire,  of  20  feet  per  second.  During  the  next  second 
this  side  velocity  will  increase  to  40  feet  per  second,  during 
the  next  to  60  feet,  and  so  on;  while  all  the  time  the  forward 
velocity  will  be  decreasing.  It  is  quite  conceivable  that 
if  the  range  were  long  enough  and  the  twist  sharp  enough 
the  shell  would  end  by  drifting  almost  square  across  the  line 
of  fire. 

A good  instance  of  drift  is  the  behavior  of  a sliced  golf 
ball.  Here  we  have  a projectile  roughened  so  that  the  effect 
of  the  twist  makes  itself  fully  felt,  a comparatively  low  veloc- 
ity, and  a sharp  spin;  and  the  result  is  often  that  the  ball 
pitches  nearly  as  far  off  the  course  as  it  carries  from  the  tee. 

It  must  not  be  supposed  that  the  above  is  either  a full  ac- 
count or  a mathematically  correct  statement  of  the  behaAuor 
of  a rifled  projectile.  It  merely  fiirnishes  a working  h3-pothesis 
sufficiently  near  the  truth  for  the  purposes  of  the  practical 
gunner. 

Persistence  of  Spin. — It  was  formerly  supposed  that  the 
spin  of  the  shell  was  but  little  affected  by  the  air-resistance, 
and  that,  for  flat  trajectories,  the  spin  continued  almost 
undiminished  to  the  end  of  the  shell’s  flight.  Recent  experi- 
ments with  mechanical  fuses  depending  for  their  action  on 


EXTERIOR  BALLISTICS 


135 


the  spin  of  the  shell  have  caused  this  view  to  be  modified. 
It  is  found  that  a R.  F.  field  shell  loses  about  10  per  cent, 
of  its  spin  at  3,000  yards,  and  about  20  per  cent,  at  5,000  yards. 

The  reasons  for  this  are  as  follows: 

I.  Part  of  the  spin  is  expended  in  overcoming  the  surface 
friction  of  the  shell  against  the  air.  It  must  be  remembered 
that  the  shell  is  constantly  passing  through  a wave  of  air 
compressed  by  its  own  forward  motion.  As  may  be  seen  from 
spark  photographs,  this  wave  of  compression  extends  beyond 
the  shoulders  of  the  shell  and  a considerable  distance  down 
the  body.  The  friction  caused  by  the  shell  rotating  in  this 
compressed  air  is  much  greater  than  it  would  be  in  air  at  the 
normal  pressure. 

II.  Part  of  the  spin  is  expended  in  giving  the  lateral 
drift  to  the  shell.  Suppose  a shell  drifts  two  degrees  at  4,000 
yards,  it  will  have  moved  400  feet  laterally  in  10  seconds, 
its  mean  lateral  velocity  will  be  40  fs.,  and  its  final  lateral 
velocity  80  fs.  If  the  shell  weighs  15  pounds,  the  energy 
consumed  in  giving  it  a lateral  velocity  of  80  fs.  will  be 

1 5 Y 400 

— — or  nearly  1,500  foot  pounds.  How  much  of 

J.D  X DjT:UU/ 

this  is  at  the  expense  of  the  forward  velocity,  and  how  much  at 
the  expense  of  the  spin,  it  is  difficult  to  say. 

III.  When  the  shell  rotates  eccentrically,  and  is  noisy 
in  flight,  the  spiu  has  to  do  a considerable  amount  of  work 
in  setting  air-waves  in  motion.  Theoretically,  therefore, 
a noisy  shell  should  drift  less  than  a steady  one,  since  it  loses 
its  spin  earlier.  But  the  flight  of  a noisy  shell  is  usually  so 
erratic  as  to  render  it  difficult  to  test  this  point. 

IV.  If  a shell  were  fired  in  vacuo,  it  would  maintain  its 
original  angle  to  the  horizontal  all  the  way,  and  would  come 
down  on  one  edge  of  its  base,  since  there  is  nothing  to  make 
it  change  its  direction.  When  it  is  fired  in  air,  its  cylindro- 
conical  shape  keeps  it  more  or  less  point  first  all  the  way. 


136 


GUNNERY 


at  least  for  flat  trajectories.  Now  it  requires  a considerable 
effort  to  change  the  direction  of  the  axis  of  the  rotating  body, 
and  this  effort  is  exerted  partly  by  the  forward  motion  of 
the  shell,  partly  by  its  spin,  reacting  on  the  cushion  of  com- 
pressed air  surrounding  the  shell.  It  is  not  therefore  sur- 
prising to  find  that  a howitzer  shell  fired  at  a high  elevation 
and  long  range  has  but  little  spin  left  at  the  end  of  its  flight, 
since  if  fired  at  45  degrees  the  axis  of  rotation  has  been  deflected 
through  more  than  a right  angle. 


PART  IV 


SHRAPNEL 


SHRAPNEL 


Description. — The  most  important  projectile  of  the  light 
artillery  is  the  shrapnel.  In  the  lecture  on  the  subject  of 
Corrector  the  manner  of  securing  the  maximum  effect  of 
shrapnel  is  fully  discussed.  Here  let  us  see  what  that  effect  is. 

A full  description  of  the  mechanical  features  of  the  shrapnel 
is  given  in  the  Handbook  of  the  3-inch  Field  Artillery  Mate- 
rial. Suffice  it  to  say  here  that  the  case  is  of  drawn  steel 
with  solid  base.  The  mouth  of  the  case  is  closed  by  an  alumi- 
num head  screwed  in  and  tapped  to  take  the  service  combi- 
nation time  and  percussion  fuse.  The  burstmg  charge  is 
2M  ounces  of  loose  black  powder;  it  is  placed  in  the  base, 
and  covered  by  a steel  diaphragm.  The  diaphragm  supports 
a steel  central  tube,  which  extends  forward  through  the 
aluminum  head  to  the  fuse,  and  thus  affords  a conduit  for 
the  flames  to  the  bursting  charge.  At  the  lower  end  of  the 
central  tube  a stopper  of  dry  guncotton  is  fltted,  to  prevent 
the  loose  powder  charge  from  getting  into  the  tube,  and 
also  to  help  the  ignition  of  the  bursting  charge. 

The  shrapnel  filling  is  composed  of  252  balls,  each  .49 
inch  in  diameter  and  approximately  167  grains  in  weight 
or  42  to  the  pound.  The  balls  are  assembled  around  the  central 
tube  and  rest  upon  the  steel  diaphragm,  the  interstices  con- 
taining a smoke-producing  matrix.  This  matrix  serves  not  only 
to  hold  all  the  parts  securely  in  place,  but,  on  explosion,  makes 
a clearly  visible  burst  and  so  facilitates  observation  of  fire. 

Bursting  of  Shrapnel. — The  weakest  cross-section  is  at 
the  line  of  attachment  of  the  head,  therefore,  when  the  shrapnel 
bursts  the  balls  are  expelled  forward  and  downward  with 
increased  velocity,  and  as  they  have  at  the  same  time  the 

139 


140 


GUNNERY 


movement  of  rotation  of  the  projectile  they  are  dispersed 
more  or  less  to  the  right  and  left.  The  case  and  fuse  fall 
to  earth  about  25  yards  from  the  point  of  burst  and  serve  as 
small  solid  shot.  The  paths  of  the  pellets  form  a cone,  called 
the  cone  of  dispersion,  about  the  prolongation  of  the  trajec- 
tory. This  cone  approximates  that  which  proceeds  from  a 
garden-hose  sprinkler.  If  the  nozzle  of  the  sprinkler,  which 
may  be  considered  as  the  shrapnel  case,  is  held  in  a horizontal 
position,  it  is  obvious  that  more  ground  will  be  watered  than  if 
the  nozzle  is  inclined  downward.  And  so,  if  the  shrapnel  is 
moving  more  nearly  horizontally,  as  at  short  ranges,  than  verti- 
cally in  its  fall,  as  at  long  ranges,  more  ground  will  be  searched 
by  the  pellets.  It  is  also  evident  that  if  the  nozzle  be  held  high 
in  the  air  a larger  surface  will  be  sprinkled  since  the  spray  has 
more  time  to  spread  out  before  the  water  strikes  the  ground. 

Cone  of  Dispersion. — The  section  of  this  cone  where  it 
is  intersected  by  the  ground  is  an  irregular  oval,  its  dimensions 
varying,  as  is  evident,  with  the  angle  of  fall,  the  height  of 
burst,  and  the  relation  between  the  velocities  of  translation 
and  rotation  at  the  moment  of  burst. 

The  greater  the  velocity  of  translation  the  greater  will  be 
the  velocity  of  the  pellets  and  consequently  the  longer  the 
oval  in  the  direction  of  translation. 

The  greater  the  velocity  of  rotation  the  greater  the  lateral 
dispersion  of  the  pellets,  which  increase  the  width  of  the 
oval,  the  pellets  traveling  further  at  right  angles  to  the  tra- 
jectory before  they  strike  the  ground. 

The  width  of  the  cone  of  dispersion  is  about  20  yards  for  all 
ranges.  Hence  the  guns  of  a battery  are  spaced  20  yards  apart. 

Effective  Zone. — It  is  assumed  that  when  a shrapnel  ball 
has  an  energy  of  58  foot-pounds  it  has  sufficient  force  to 
disable  a man,  and  with  287  foot-pounds  of  energy  it  vdll 
disable  a horse.  These  energies  correspond  in  the  service 
shrapnel  bullet  to  velocities  of  about  400  and  880  foot-seconds. 
An  increased  velocity  of  from  250  to  300  feet  is  imparted  to 


SHRAPNEL 


141 


the  balls  by  the  bursting  charge.  Knowing  the  velocity  of  the 
projectile  and  the  weight  of  the  balls  the  space  within  which 
the  balls  will  be  effective  may  be  determined  for  any  range. 

While  the  service  muzzle  velocity  is  1,700  fs.  the  remaining 
velocity  of  the  shrapnel  at  6,500  yards  is  only  700  fs.  It  is 
seen,  then,  that  the  remaining  velocity  decreases  as  the  range 
increases,  and  so  necessarily  the  resultant  velocity  of  the  pellets 
decreases  as  the  range  increases.  This  decrease  in  velocity, 
added  to  the  effect  of  a large  angle  of  fall  which  tends  to  tilt 
the  nozzle  downward,  accounts  for  the  shallow  depth  of  the 
cone  of  dispersion  at  long  ranges. 

The  loss  of  velocity  and  the  inclination  of  the  nozzle,  so  to 
speak,  at  long  ranges  are  compensated  for  somewhat  by  increas- 
ing the  height  of  burst  as  the  range  increases.  The  most  effec- 
tive pattern  cannot  however  be  maintained  by  this  means. 
The  compensation  is  only  partial.  A simple  well-adjusted 
shrapnel  covers  effectively  an  area  200  yards  in  depth  up 
to  3,000  yards.  Beyond  this  range  the  depth  diminishes  until 
at  4,500  yards  the  beaten  zone  is  but  125  yards  deep. 

Point  of  Burst  and  Interval  of  Burst. — The  best  point  of 
burst  for  a shrapnel  is  assumed  to  be  that  point  from  which 
the  burst  of  the  shrapnel  will  produce  practically  one  hit 
per  square  yard  of  vertical  surface  at  the  target.  It  is  deter- 
mined from  the  cone  of  dispersion  by  finding  the  vertical 
section  which  cut  through  the  cone  will  contain  as  many 
square  yards  as  there  are  pellets  in  the  shrapnel.  The  dis- 
tance in  front  of  the  target  at  which  the  burst  occurs  is  called 
the  interval  of  burst.  On  account  of  the  variations  at  dif- 
ferent ranges  in  the  velocities  of  translation  and  of  rotation 
the  interval  of  burst  which  will  produce  one  hit  per  square 
yard  of  vertical  surface  at  the  target  varies  with  the  range, 
decreasing  as  the  range  increases. 

Practically  it  is  found  best  to  consider  the  height  of  burst 
rather  than  the  interval  of  burst,  since  the  battery  commander 
can  more  readily  estimate  the  height  than  the  interval.  Suit- 


142 


GUNNERY 


able  cross-hairs  in  the  field  of  the  battery  commander’s 
telescope  facilitate  this  estimation. 

In  oitr  service  a height  of  3-1000  of  the  range,  called  3 
mils,  is  adopted  as  the  most  favorable  mean  height  of  burst. 
The  point  of  burst  at  this  height  gives,  over  a large  part  of 
the  range,  very  approximately  the  correct  interval  of  burst. 
For  short  ranges  this  height  of  burst  is  excessive,  and  for 
long  ranges  it  is  insufficient. 

The  following  table  shows  for  the  3-inch  shrapnel  the 
results  obtained  at  different  ranges  from  bursts  at  the  correct 


Range. 

One  Hit  per  Sq.  Yd. 

Height  of  Burst,  3 MUs. 

Interval. 

Front  Covered. 

Interval. 

Front  Covered. 

Yards. 

Yards. 

Yards. 

Yards. 

Yards. 

1,000 

81.4 

18.5 

118.2 

27.0 

2,000 

73.0 

18.5 

83.4 

21.2 

2,500 

68.98 

18.5 

73.5 

19.55 

3,000 

65.84 

18.5 

66.6 

18.76 

3,500 

63.28 

18.5 

60.9 

18.84 

4,000 

61.07 

18.5 

56.4 

17.12 

4,500 

58.97 

18.5 

51.3 

16.13 

interval  of  burst,  and  also  at  a height  of  burst  of  3 mils.  The 
front  of  target  that  should  be  covered  depends  upon  the  number 
of  balls  in  the  shrapnel.  For  the  3-inch  shrapnel  with  270 
bullets,  a former  model,  the  front  to  be  covered  with  one 
hit  per  square  yard  is  18.5  yards. 

It  will  be  observed  that  between  2,000  and  4,500  yards 
the  height  of  burst  of  3 mils  gives  approximately  the  desired 
density  of  fire  at  the  target.  At  ranges  less  than  2,000  yards 
the  front  covered  is  largely  increased  and  the  density  of 
fire  therefore  diminished. 

The  figures  refer  to  a single  shrapnel  bursting  at  the  mean 
point  of  burst.  In  a group  of  shrapnel  the  bursts  above  and 


SHRAPNEL 


143 


below  the  mean  point  would  largely  make  up  the  discrepan- 
cies in  distribution  and  density. 

On  account  of  errors  of  gun  and  fuse  the  dispersion  of 
several  rounds  is  also  a little  greater.  Experiments  have 
shown  that  volley  fire,  two  or  more  rounds  per  gun,  will  cover 
a beaten  zone  about  250  yards  deep  at  3,000  yards  range, 
and  150  yards  deep  at  4,500  yards. 

WTiile  it  is  possible,  then,  to  deliver  an  accurate  fire  at 
a range  of  7,000  yards,  the  effectiveness  of  shrapnel  fire 
diminishes  with  the  increase  of  the  range  from  3,000  yards 
on.  At  extreme  ranges  the  possibility  of  putting  permanently 
out  of  action  an  opposing  battery,  concealed  from  view  and 
having  its  personnel  protected  by  shields,  is  very  remote. 

The  battery  may  be  temporarily  silenced  or  forced  to 
slacken  its  fire,  but  during  the  calm  after  the  squall  its  power 
vfill  be  found  little  impaired,  for  at  such  ranges  the  shrapnel 
has  very  little  sweeping  power  and  consequently  the  danger 
space  is  small.  It  must  almost  light  on  an  object  to  injure  it. 

Experimental  Tests. — Experimental  firing  in  1906  estab- 
lished the  following  facts  concerning  accurately  adjusted 
shrapnel  fire  (3  mils  height  of  burst)  at  a range  of  3,000  yards : 

19%  of  the  shrapnel  will  burst  on  graze. 

20%  will  burst  less  than  9 yards  in  front  of  the  target, 
all  of  which  distance  is  danger  space  for  men  standing. 

50%  will  burst  less  than  66  yards  from  the  target;  danger 
space,  45  yards. 

75%  will  burst  less  than  111  yards  from  the  target;  danger 
space,  84  yards. 

95%  will  burst  less  than  163  yards  from  the  target;  dan- 
ger space,  103  yards. 

95%  will  burst  less  than  190  yards  from  the  target;  dan- 
ger space,  118  yards 

99%  vfill  burst  less  than  242  yards  from  the  target;  dan- 
ger space,  149  yards. 


144 


GUNNERY 


From  these  figures  it  may  be  determined  what  area  in 
front  of  an  objective  point  is  searched  by  well-directed  shrap- 
nel fire.  There  will  be  premature  bursts  much  further  from 
the  target  than  shown  by  the  foregoing  figures  which  would 
endanger  the  advance  of  troops  being  supported  by  the  fire. 

The  interval  between  the  point  of  burst  of  a shrapnel 
and  the  target  is  called  the  interval  of  burst.  It  is  plus  ( + ) 
or  minus  ( — ) according  as  the  shot  is  over  or  short.  The 
distance  of  the  normal  burst  from  the  target  is  the  mean 
interval  of  burst,  and  depends  upon  the  range,  and,  there- 
fore, the  height  of  the  mean  burst. 

The  following  facts  have  also  been  ascertained  by  experi- 
ment. 

The  time  fuse  acts  with  a considerable  degree  of  uni- 
formity. The  error  of  the  fuse  is,  however,  much  too  great. 
At  mid-ranges  about  20%  of  the  shrapnel  fired  will  burst 
on  graze  even  though  the  fire  has  been  well  adjusted.  They 
are  then,  as  a rule,  quite  ineffective.  Moreover,  about  10% 
to  15%  will  burst  so  high  as  to  be  almost  ineffective.  Thus, 
due  to  the  error  of  the  fuse,  about  30%  of  the  fii’e  is  practically 
ineffective  at  favorable  ranges  and  30%  of  the  ammunition 
is  wasted  by  reason  of  a defect  in  one  part  of  the  projectile. 

Artillery  efficiency  is  measured  by  its  ability  to  burst 
effective  shrapnel  at  the  target,  and  for  this  purpose  the  whole 
expensive  plant  in  men,  animals  and  material  is  maintained. 
Assuming  that  the  personnel  is  capable  of  performing  its 
part  perfectly,  the  measure  of  efficiency  would  still  depend 
upon  the  accuracy  of  the  fuse.  The  fuse  is  the  weak  point 
in  the  present  system.  The  “hooded-vent”  fuse,  with  a 
reducer  error,  has  been  adopted  since  the  tests  of  1906; 
but  the  error  is  not  much  less  than  that  of  the  earlier  tjq^e, 
and  the  foregoing  figures  are  practically  five. 

About  5%  of  the  shrapnel  cases  burst  in  air. 

Shrapnel  seldom  break  up  in  the  gun  or  burst  at  the  muzzle. 

About  K of  the  pellets  are  ineffective  at  all  ranges. 


SHRAPNEL 


145 


The  normal  height  of  3 mils  gives  the  most  favorable 
distribution  of  effect,  when  targets  of  all  kinds  are  considered, 
that  is,  the  density  of  fire  approaches  most  nearly  to  one 
hit  per  unit  of  surface. 

A lower  burst  gives  very  dense  effect  over  a restricted  area, 
but  the  bullets  are  not  used  economically;  two  or  three  being 
expended  to  do  the  work  of  one. 

A greater  height  of  burst  increases  the  width  and  depth 
of  the  bullet  pattern,  and  permits  utilizing  the  full  effective 
range  of  the  bullets;  but  the  density  of  fire  decreases,  and  the 
proportion  of  ineffective  hits  increases  very  rapidly  with  the 
height  of  burst.  Hence,  the  area  is  not  effectively  searched. 
It  is  to  be  noted,  however,  that  against  deep,  broad  targets 
it  is  preferable  to  have  the  mean  height  of  burst  a little  high 
rather  than  too  low,  as  the  former  gives  a better  distribution 
of  the  effect. 

Bursts  on  graze  are  practically  ineffective  unless  within 
10  yards  of  the  target. 

The  projectile  will  ricochet  up  to  3,700  yards  and  burst 
after  graze  is  obtained.  At  longer  ranges  the  projectile  does 
not  seem  to  ricochet,  but  enters  the  ground  and  bursts  after 
penetrating  several  feet,  creating  a large  crater.  There  were 
instances  in  the  Russo-Japanese  War  of  shrapnel  penetrating 
9 inches  of  masonry  before  bursting. 

High  Explosive  Shrapnel. — A more  powerful  shrapnel 
than  the  one  now  in  general  use  in  our  service  is  being 
perfected.  It  is  known  as  a single- type  projectile,  that 
is,  it  is  designed  to  be  used  either  as  a shrapnel  or  as  a 
high  explosive  shell.  This  is  accomplished  in  the  following 
way:  The  matrix  in  which  the  pellets  are  imbedded,  instead 
of  being  an  inert  substance,  or  merely  a smoke-producing 
material  as  in  the  common  shrapnel,  is,  in  itself,  a high 
explosive.  This  high  explosive,  however,  is  very  insensitive, 
so  that,  when  the  shrapnel  is  discharged  in  the  air  by 
the  burning  of  the  small  black  powder  charge  in  its  base, 


146 


GUNNERY 


the  high  explosive  is  not  detonated  or  exploded.  In  order 
to  cause  the  detonation  of  the  matrix  when  the  projectile 
bursts  on  percussion,  the  head  of  the  projectile  has  a cham- 
ber containing  a charge  of  high  explosive.  When  the  pro- 
jectile strikes  a resisting  object,  the  percussion  element  of 
the  combination  fuse  detonates  the  charge  of  high  explosive, 
which,  in  turn,  detonates  the  high  explosive  matrix.  If  the 
projectile  bursts  in  air  the  head  is  blown  off,  and  on  striking 
acts  as  though  it  were  a small  high  explosive  shell. 

This  projectile,  if  perfected,  will  possess  many  advantages, 
as  the  difficulties  growing  out  of  several  types  of  ammunition 
would  be  eliminated  and  the  vexing  question  of  the  relative 
proportions  of  shell  and  shrapnel  would  no  longer  present  itself. 

High  Explosive  Shell. — At  present,  shrapnel  and  shell  are 
both  issued,  the  former  for  animate  and  the  latter  for  inani- 
mate objects.  The  present  shrapnel  bullet  has  not  sufficient 
power  to  destroy  material;  and  on  account  of  the  flatness 
of  the  trajectory  and  the  small  angle  of  the  cone  of  dispersion, 
it  cannot  reach  troops  in  any  but  the  lightest  entrenchments. 
Hence,  the  other  type  of  ammunition,  or  the  steel  shell,  is 
issued,  holding  about  two  pounds  of  the  service  high  explosive. 
This  is  burst  by  a detonating  percussion  fuze. 

On  detonation  of  the  filler,  the  shell  breaks  up  into  500 
to  600  fragments,  and  it  has  been  proposed  to  use  it  instead 
of  shrapnel  against  troops  in  entrencliments,  for  if  it  bursts 
at  the  proper  point,  by  means  of  a time  fuse,  the  fragments 
fly  in  all  directions  and  search  cover  in  a manner  impossible  to 
shrapnel.  No  satisfactory  results  of  this  nature  have  been  ob- 
tained, however,  and  so  no  time-shell  is  issued  in  our  ser\dce. 

The  explosive  used  in  the  H.  E.  shell  is  a secret  compound, 
and  combines  extreme  safety  in  transportation  vdth  extreme 
certainty  and  force  of  action.  The  shell  complete  weighs 
the  same  as  the  shrapnel,  18.75  pounds.  The  projectile 
in  each  case  weighs  15  pounds;  the  high  explosive  power  of 
the  shell  compensating  for  its  lightness  in  metal. 


PART  V 


PRACTICAL  GUNNERY 


Chapter 

U 

a 

tc 

u 

t( 


I.  Fire  and  Fire  Data. 

II.  Indirect  Fire  and  Deflection. 

III.  Range  and  Ranging. 

IV.  Angle  of  Site. 

V.  Corrector. 

VI.  Observation  of  Fire. 

VII.  Position  and  the  Mask. 


147 


i 

i 


] 


/ 


1 


\ 


I 


PRACTICAL  GUNNERY 


CHAPTER  I 
FIRE  AND  FIRE  DATA 

The  Sheaf  of  Fire. — When  the  fire  of  a number  of  guns 
is  directed  upon  any  object  the  line  of  fire  of  each  gun  forms 
with  the  others  a bent  cone,  called  the  sheaf  of  fire.  Due 
to  the  varying  inaccuracies  of  the  gun  it  is  practically  impos- 
sible to  cause  all  the  projectiles  to  light  at  the  same  point. 
Each  battery  salvo,  therefore,  searches  a slightly  different 
area  from  the  other,  which  is  beneficial  rather  than  unde- 
sirable. 

A battery  may  be  likened  to  the  human  hand,  in  that  the 
sheaf  of  fire,  represented  by  the  fingers,  may  be  shifted  to 
the  right,  left,  up  or  down,  by  the  movement  of  the  wrist, 
or  the  sheaf  may  be  opened  out,  closed,  or  maintained  at  the 
parallel,  by  the  movement  of  the  four  fingers.  It  is  the  abil- 
ity to  shift  the  sheaf  of  fire  rapidly,  and  direct  the  fingers, 
so  to  speak,  at  the  target,  that  constitutes  a skilled  gunner. 
When  this  can  be  done  with  speed  and  accuracy,  under  the 
varying  circmnstances  encountered  in  the  field,  a battery 
is  capable  of  dehvering  an  effective  fire.  If  this  cannot  be  done, 
the  hand  is  paralyzed,  and  so  the  battery  cannot  perform 
its  function. 

When  a man  points  his  forefinger  at  an  object,  the  mind 
controls  the  movement.  The  muscular  movement  of  the 
hand  and  arm  is  more  or  less  involuntary.  It  is  not  necessary 
to  concentrate  the  mind  upon  the  movement  of  the  arm  and 


149 


150 


GUNNERY 


hand,  but  only  upon  the  object.  And  so  it  should  be  in  the 
case  of  a battery  commander  in  directing  the  sheaf  of  fire. 
The  calculation  of  the  necessary  data  should  be  a matter  of 
second  nature  with  him  to  such  an  extent  that  the  most 
unexpected  developments  will  not  disturb  the  habit  of  his 
mind  and  thereby  destroy  the  sheaf  of  fire. 

Fire  Control  and  Direction. — The  officer  who  has  charge 
of  the  auxiliary  arm  of  artillery  is  said  to  “control”  the 
fire.  Under  his  authority  as  the  controlling  officer  he  generally 
assigns  a certain  portion  of  the  hostile  terrain  to  a group 
of  guns.  That  portion  so  assigned  a particular  group  is  said 
to  be  its  sector  of  fire.  The  officer  in  command  of  the  group 
“directs”  the  fire  of  his  guns  within  the  sector  assigned  him. 
There  may  be  a number  of  hostile  positions  within  any  sector. 
If  any  of  these  positions  are  occupied  by  groups  of  artillery, 
the  one  aim  of  the  officer  directing  the  fire  is  to  secure  a supe- 
riority of  fire  over  the  hostile  guns.  This  may  be  frequently 
done  even  though  the  number  of  his  guns  is  less  than  that  of 
the  enemy.  For  instance,  the  directing  officer  may  have 
a much  more  perfect  knowledge  of  the  hostile  position  than 
the  enemy  has  of  the  firer’s  position.  In  such  a case  he 
may  shift  the  sheaf  of  fire  of  all  his  guns  from  one  hostile 
position  to  another,  alternately  subduing  the  enemy’s  fire, 
whereas  the  hostile  fire  is  scattered  and  more  or  less  ineffec- 
tive, due  to  the  enemy’s  ignorance  as  to  the  exact  position 
of  the  opposing  guns.  The  method  of  delivering  a rapid 
fire  in  sudden  bursts  of  short  duration  is  called  the  “Squall 
Method,”  and  is  obviously  more  effective  than  the  old  method 
of  prolonged  fire  at  a slower  rate.  It  is  also  more  economical 
in  the  expenditure  of  ammunition. 

If  a battery  or  group  open  with  inaccurate  data,  its  posi- 
tion is  at  once  exposed  to  a watchful  and  well-informed  enem}", 
and  before  the  fire  can  be  adjusted  a weak  opponent  will 
withdraw  to  a new  position  and  open  fire,  or  a relativeh" 
strong  opponent  will  attain  superiority. 


FIRE  AND  FIRE  DATA 


151 


The  necessity  of  obtaining  accurate  data  before  opening 
fire  is  quite  apparent,  for  the  enemy,  once  having  attained 
the  ascendancy,  will  render  its  opponent  ineffective  altogether 
or  force  a change  of  position  on  the  latter’s  part. 

It  is  often  advisable  to  adjust  the  fire  upon  a position 
somewhat  removed  from  the  one  to  be  eventually  attacked, 
and  then  to  suddenly  shift  the  adjusted  sheaf  upon  the  hos- 
tile position.  This  eliminates  the  danger  of  alarming  a weak 
opponent,  who  may  be  successfully  destroyed,  and  in  a measure 
prevents  the  disclosure  of  position  to  a more  worthy  opponent. 

Now  in  order  to  be  able  to  direct  the  fire,  and  shift  the 
sheaf  from  point  to  point,  it  is  necessary  to  become  thoroughly 
familiar,  not  only  with  the  practical  means  employed,  but 
with  the  theory  upon  which  the  practice  is  based. 

Inaccuracy  of  Fire. — However  perfectly  a gun  may  be 
laid,  it  is  practically  impossible  to  get  two  successive  rounds 
to  fall  in  the  same  place.  This  is  due  to  several  causes.  In 
the  first  place,  the  muzzle  velocity  varies  from  round  to  round, 
owing  to  irregularities  in  the  powder  charge  and  its  combus- 
tion, and  in  the  resistance  of  the  driving  band.  Next,  the 
varying  jump  of  the  gun  causes  deviations  in  elevation.  And 
if  the  carriage  be  on  a lateral  slope,  or  if  one  wheel  be  on 
bad  ground,  the  jump  causes  errors  of  direction  as  well. 
In  the  next  place,  the  projectile  rarely  comes  out  of  the  muz- 
zle quite  straight,  but  usually  with  its  nose  pointing  somewhat 
away  from  the  line  of  departure,  and  revolving  around  it. 
This  causes  the  projectile  to  describe  a corkscrew-curve 
around  the  actual  trajectory.  The  amount  of  the  wobble 
tends  to  decrease  under  the  influence  of  the  resistance  of 
the  air,  till  at  about  1,000  yards  the  projectile  begins  to  settle 
down  to  a regular  curve.  In  the  same  way  a spinning  top, 
after  a first  period  of  wobbling,  “goes  to  sleep,”  and  remains 
steady  till  its  spin  is  insufficient  to  resist  the  overturning 
movement  due  to  the  frictional  resistance  of  its  point. 

A further  important  cause  of  inaccuracy  is  defective 


152 


GUNNERY 


manufacture.  If  the  wall  of  the  projectile  be  thicker  at  one 
side  than  at  the  other,  the  center  of  gravity  will  not  be  in 
the  axis  of  the  shell,  and  its  rotation  will  cause  the  shell  to 
wobble. 

Besides  these  sources  of  error,  the  flight  of  the  shell  will  be 
affected  by  the  varying  wind  which  it  happens  to  encounter. 
Rough  corrections  in  deflection  for  windage  are  prescribed 
in  the  Drill  Regulations. 

The  practical  result  of  the  combination  of  errors  is  that 
the  trajectories  of  a number  of  projectiles  fired  from  the  same 
gun  at  the  same  elevation  form  a bent  cone  (Figure  1)  which 
is  called  the  sheaf  of  fire  of  the  gun,  just  as  the  cone  of  fire 
from  the  four  guns  is  called  the  sheaf  of  fire  of  the  battery. 


The  intersection  of  the  surface  of  the  ground  with  the  sheaf 
of  fire  forms  an  ellipse,  or  oval  figure,  of  which  the  breadth  is 
equal  to  the  diameter  of  the  cone,  while  the  length  or  major 
axis  increases  with  the  smallness  of  the  angle  of  descent. 

The  more  accurate  the  gun  the  smaller  the  ellipse.  The 
accuracy  of  a gun  at  any  range  is  determined  as  follows: 

A number  of  shots  are  fired  under  the  given  conditions, 
care  being  exercised  to  make  the  circumstances  of  all  the  rounds 
as  nearly  alike  as  possible.  The  point  of  fall  of  each  shot 
is  plotted  on  the  chart  or  marked  on  the  target  when  practi- 
cable. The  target  may  be  either  horizontal  or  vertical. 

The  numerical  sum  of  the  horizontal  de\dations  dhdded 
by  the  number  of  shots  is  the  mean  horizontal  de\dation. 


FIRE  AND  FIRE  DATA 


153 


The  mean  vertical  deviation  is  similarly  obtained  from  the 
numerical  sum  of  the  vertical  deviations. 

The  actual  distance  of  each  shot  from  the  center  of  impact 
is  the  absolute  deviation  for  the  shot,  and  the  mean  of  the  abso- 
lute deviations  is  the  mean  absolute  deviation  of  the  group. 

By  comparing  the  mean  absolute  deviations  of  different 
groups  of  shots  we  may  arrive  at  the  comparative  accuracy  of 
different  guns  or  of  the  same  gun  under  different  conditions 
of  loading  and  firing. 

Since  the  effect  of  the  same  error  is  greater  for  long  ranges 
than  for  short,  it  is  apparent  that  fire  at  long  ranges  is  more 
inaccurate  than  for  short.  Since  long-range  fire  is  not  only 
less  effective  than  short-range  fire,  but  is  also  less  accurate, 
we  can  see  that  the  practical  gunner  must  employ  every 
form  of  ingenuity  to  shove  his  guns  into  close  proximity  to 
the  enemy.  The  great  mistake  was  made  of  fighting  field 
guns  at  too  long  ranges  in  the  Russo-Japanese  War.  Neuffer 
tells  us  that  the  use  of  the  mask  was  not  well  understood.^ 

Percussion  Fire. — Percussion  fire  is  principally  employed 
for  the  destruction  of  material  objects,  such  as  walls,  build- 
ings, obstacles,  artillery  material,  etc.  Such  fire  is  termed 
fire  for  demolition.  An  accurate  adjustment  in  range  is 
requisite. 

For  the  destruction  of  artillery  material  or  other  targets 
of  low  relief,  light  field  guns  should  habitually  be  approached 
within  2,500  yards  of  their  target. 

The  usual  procedure  is  to  obtain  a 100-yard  bracket  and 
to  fire  enough  rounds  at  the  limits  of  this  bracket  to  deter- 
mine definitely  that  fire  at  the  near  limit  is  short  and  that 
fire  at  the  further  limit  is  over.  One  or  more  battery  salvos 
are  ordinarily  required  for  this  purpose.  The  bracket  having 
been  established,  continuous  fire  is  begun  at  the  mid  range 
of  the  bracket.  If  observation  of  a considerable  number  of 

* Lieutenant  William  Neuffer,  Third  Bavarian  (Prince  Leopold)  Regiment 
of  Field  Artillery.  (Artilleristische  Monatschefts  No.  35,  November,  1909.) 


154 


GUNNERY 


rounds  at  the  mid  range  indicates  that  the  mean  point  of 
burst  is  still  short  or  over,  the  range  is  changed  by  25  yards  in 
the  appropriate  sense.  Changes  of  range  of  less  than  25 
yards  should  not  be  made. 

Percussion  fire  is  considered  adjusted  when  it  is  e\ddent 
that  effect  is  being  produced  upon  the  target  and  when  the 
proportion  of  shorts  and  overs  is  sensibly  even. 

Time  Fire. — Time  fire  is  employed  for  the  attack  on  ani- 
mate objects.  The  nature  of  the  target  and  the  conditions 
affecting  observation  of  fire  determine  the  limits  within 
which  the  range  may  be  found. 

When  the  target  consists  of  troops  immobilized  in  position 
— as,  for  example,  infantry  in  trenches,  artillery  in  battery, 
etc. — a 100-yard  bracket  is  always,  if  possible,  obtained. 

If  the  conditions  are  favorable  for  observation,  the  exact 
adjustment  of  the  fire  may  be  at  once  undertaken,  as  explained 
in  the  case  of  percussion  fire.  Before  passing  to  fire  for  effect, 
however,  salvos  are  fired  at  the  mid  range  of  the  bracket 
for  the  final  adjustment  of  the  height  of  burst  and  the  dis- 
tribution. The  fire  for  effect  may  be  by  continuous  fire  or 
by  volleys. 

But  if  the  conditions  are  unfavorable  for  observation,  it 
is  preferable,  after  adjusting  the  height  of  burst  and  distribu- 
tion, to  direct  the  fire  for  effect  successively  at  the  short,  mid, 
and  long  ranges  of  the  bracket  until  it  can  be  definitely  deter- 
mined at  which  range  the  fire  is  most  effective.  Salvos,  con- 
tinuous fire,  or  volleys  may  be  used  for  the  purpose. 

If  a 100-yard  bracket  cannot  be  sm’ely  obtained,  then  the 
bracket  obtained  may  similarly  be  searched  by  successive 
increments  or  decrements  of  50  or  100  yards  in  the  range  until 
it  can  be  definitely  determined  at  which  range  the  fire  is 
most  effective. 

Time  fire  is  considered  adjusted  when  it  is  evident  that 
effect  is  being  produced  upon  the  target;  when  the  great  pro- 
portion of  bursts  in  air  are  short  of  the  target  and  at  the  proper 


FIRE  AND  FIRE  DATA 


155 


mean  height;  when  the  shrapnel  cases  are  seen  to  strike  at  or 
near  the  target;  when  dust,  if  seen  at  all,  is  knocked  up  by 
the  bullets  both  in  front  and  in  rear  of  the  target;  and  when 
a due  proportion  of  bursts  on  graze  occur  and  such  bursts  are 
about  evenly  divided  between  shorts  and  overs. 

When  the  target  consists  of  troops  moving  or  liable  to 
move,  the  smallest  bracket  is  obtained  which  can  be  surely 
and  quickly  established,  and  its  depth  is  then  promptly 
searched  by  the  subsequent  fire. 

The  usual  procedure  in  such  cases  is  to  obtain  quickly  by 
bold  changes  of  range  a large  but  unmistakable  bracket;  to 
narrow  this  bracket  to  200  or  to  100  yards  if  the  conditions 
permit;  to  fire  verifying  salvos  at  the  short  limit  of  the  bracket, 
if  the  height  of  burst  and  distribution  have  not  already  been 
adjusted  during  the  bracketing  series;  and  then  to  employ 
volleys  or  salvos  at  successive  ranges,  or  zone  fire  to  search 
the  bracket. 

Volleys  or  salvos  at  successive  ranges  may  be  employed  to 
search  an  area  of  any  desired  depth.  The  range  ordered  for 
the  first  volley  or  salvo  is  usually  that  corresponding  to  the 
short  limit  of  the  bracket.  The  fire  is  then  continued  pro- 
gressively until  the  opposite  limit  of  the  bracket  is  reached  by 
changes  of  50  to  100  yards  in  range  from  volley  to  volley  or 
from  salvo  to  salvo,  the  time  interval  between  volleys  or  salvos 
being  such  as  the  officer  conducting  the  fire  may  deem  appro- 
priate. A range  increment  (or  decrement)  of  50  yards  is 
ordinarily  used  if  a 100-yard  bracket  is  established,  of  100 
yards  if  a longer  bracket  is  established. 

Zone  Fire  is  especially  adapted  to  searching  quickly  the 
depth  of  a 200-yard  bracket.  It  is  not  employed  for  lesser 
depths.  If  the  depth  to  be  searched  is  much  greater  than 
200  yards,  a second  rafale  is  fired  to  extend  the  effect  in  depth. 
The  initial  range  of  a rafale  of  zone  fire  is  usually  taken  as 
100  yards  less  than  the  short  limit  of  the  bracket;  but  if  the 
target  is  obviously  moving  away  from  the  guns,  or  if,  in  the 


156 


GUNNERY 


attack  of  a stationary  target,  it  is  perfectly  clear  from  the  lay 
of  the  ground  that  fire  short  of  the  short  limit  of  the  bracket 
would  be  wasted,  then  the  short  limit  of  the  bracket  may  be 
taken  as  the  initial  range. 

If  the  ground  to  be  searched  has  a noticeable  slope  either 
to  the  front  or  rear,  and  indirect  laying  is  to  be  employed,  the 
angle  of  site  will  vary  for  different  parts  of  the  area  to  be 
searched. 

In  the  case  of  zone  fire  a mean  value  of  the  angle  of  site 
is  taken,  and  a corrector  is  used  which  will  give  low  bursts  at 
the  near  limit  of  the  zone  if  the  slope  is  away  from  the  guns, 
and  bursts  slightly  above  the  normal  height  if  the  slope  is 
toward  the  guns. 

In  the  case  of  volleys  or  salvos  at  successive  ranges  the 
same  procedure  may  be  employed  if  the  area  to  be  searched  is 
not  deep  and  the  slope  not  great;  but  for  searching  long  and 
steep  slopes  it  is  usually  preferable  to  take  the  angle  of  site 
and  then  to  vary  the  corrector  from  volley  to  volley  or  from 
salvo  to  salvo,  increasing  it  if  searching  up  the  slope,  decreas- 
ing it  if  searching  down  the  slope.  A change  of  two  points 
in  the  corrector  from  volley  to  volley  or  from  salvo  to  salvo 
will  suffice  in  the  usual  case. 

Whenever  searching  fire  is  employed  it  must  be  carefully 
observed  with  a view  to  securing  a closer  adjustment  for  sub- 
sequent fire.  If  fire  at  certain  ranges  is  evidently  ineffective, 
those  ranges  are  rejected  in  the  subsequent  fire.  If  the  con- 
ditions permit,  the  process  of  bracketing  is  resumed  and  a 
closer  adjustment  secured. 

If  the  ground  either  in  front  or  in  rear  of  the  target  cannot 
be  seen,  or  if  the  target  is  totally  masked,  every  effort  must 
be  made  to  determine  as  accurately  as  possible  the  distance  of 
the  target  from  some  feature  of  the  terrain  which  is  \fisible 
to  the  officer  conducting  the  fire,  and  which  may  be  used  as  a 
registration  mark  for  the  adjustment  of  fire.  Thus  if  a target 
is  beyond  a crest  the  distance  of  the  target  from  the  crest  line 


FIRE  AND  FIRE  DATA 


157 


is  to  be  determined;  if  the  target  is  masked  by  trees  and  is  so 
situated  that  the  ground  in  rear  of  the  target  can  alone  be 
seen,  some  feature  of  the  ground  in  rear  of  the  target  may  be 
taken,  as  the  registration  mark  and  the  distance  determined 
from  it. 

In  such  cases  the  fire  is  adjusted  on  the  registration  mark 
chosen  and  then  shifted  so  as  to  search  the  area  within  which 
the  target  has  been  located.  It  is  most  important  to  have 
observers  posted  so  that  they  can  observe  the  fire  and  assist 
in  its  adjustment. 

Verifying  Salvos. — Salvos  fired  to  verify  the  firing  data  in 
use,  or  to  secure  a more  perfect  adjustment  of  the  fire  before 
passing  to  fire  for  effect,  are  termed  verifying  salvos. 

They  are  especially  appropriate  to  fully  establish  the 
limits  of  a bracket;  to  determine  definitely  whether  fire  at  a 
given  range  is  really  effective,  as  has  appeared  from  the  obser- 
vation of  previous  but  insufficient  fixe;  to  secure  the  final  adjust- 
ment in  direction,  height  of  burst,  and  range,  particularly  in 
cases  when  only  a portion  of  the  guns  have  been  used  in  the 
fire  for  adjustment. 

If  opportunity  is  afforded  during  the  bracketing  series  to 
secure  a satisfactory  adjustment  of  the  fire,  verifying  salvos 
are  unnecessary,  except  that,  in  the  case  of  a target  mo^fing 
toward  or  away  from  the  guns,  if  any  considerable  time  has 
elapsed  since  the  establishment  of  that  limit  of  the  bracket 
toward  which  the  target  is  moving,  a salvo  or  salvos  should 
be  fired  at  the  range  corresponding  either  to  that  limit  or  to 
a point  stiU  farther  in  advance  of  the  movement  of  the  target 
for  the  final  verification  of  the  range  before  passing  to  fire  for 
effect. 

Application  of  Fire. — In  service  the  fire  of  artillery  must 
be  adapted  to  meet  the  requirements  of  many  and  ever-vary- 
ing conditions.  An  infinite  variety  of  concrete  problems  is 
afforded,  and  each  problem  will  have  its  own  best  solution. 
Great  flexibility  in  the  employemnt  of  fire  is  hence  called  for. 


158 


GUNNERY 


The  Regulations  set  forth  principles  which  are  the  bases  of 
action  and  rules  which  may  serve  as  guides  in  the  average 
case;  but  the  Regulations  must  not  be  looked  to  for  ready-made 
solutions  of  the  problems  which  arise  in  service.  Having  thor- 
oughly mastered  the  principles  of  the  Regulations  and  thor- 
oughly grasped  the  possibilities  of  the  gun  and  its  equipment, 
an  officer  must  so  prepare  himself  that  he  will  be  able  to  recog- 
nize at  once  the  means  to  be  employed  in  any  concrete  case 
and  be  capable  of  putting  these  means  into  effect.  Every 
latitude  is  allowed  him  in  the  choice  of  a method  of  fire  and  in 
its  adaptation  to  the  special  case  in  hand.  By  constant  prac- 
tice in  peace  in  employing  fire  (simulated  or  otherwise)  to 
meet  the  requirements  of  a great  variety  of  tactical  situations, 
officers  may  prepare  themselves  to  use  their  guns  to  the  best 
advantage  of  war. 

The  special  characteristics  of  the  different  methods  of  fire 
provided  for  in  the  next  text  are  outlined  below,  with  some 
illustrations  of  their  applicability. 

Continuous  Fire  is  adapted  especially  to  the  demolition  of 
material  objects  and  to  the  attack  of  personnel  inactive  and 
more  or  less  fixed  in  position  and  protected  from  fire. 

The  fire  may  be  as  rapid  or  as  slow  as  desired,  thus  per- 
mitting the  expenditure  of  ammunition  to  be  exactly  regulated 
to  meet  the  requirements  of  the  case. 

Exact  adjustment  in  range  is  sought;  but  if  the  conditions 
of  observation  are  such  as  to  preclude  this,  the  smallest  pos- 
sible bracket  is  obtained  and  its  depth  searched  by  successive 
changes  in  the  range. 

Volley  Fire  is  adapted  especially  to  the  attack  of  personnel 
that  are  more  or  less  vulnerable.  The  special  characteristic 
of  this  method  of  fire  is  its  great  flexibility.  The  number  of 
volleys  to  be  fired;  their  range  difference  (if  any),  the  number 
of  rounds  in  each  volley,  are  all  in  the  hands  of  the  officer 
conducting  the  fire.  By  suitable  manipulations  of  the  sheaf 
he  may  readily  shift  the  fire  from  point  to  point  of  the  terrain 


FIRE  AND  FIRE  DATA 


159 


as  necessity  may  require,  and  by  adapting  the  bursts  of  fire 
to  meet  the  crises  of  the  action  he  may  utilize  the  ammunition 
to  the  best  advantage. 

If  exact  adjustment  in  range  can  be  obtained,  volleys  at  a 
single  range  are  employed;  otherwise  volleys  at  successive 
ranges  are  used. 

Salvos  are  adapted  especially  to  securing  the  adjustment 
of  fire.  They  may  also  be  used  for  producing  effect,  and  espe- 
cially with  the  idea  of  obtaining  at  the  same  time  additional 
information  on  which  to  base  a more  exact  adjustment  of  the 
fire.  They  are  employed  at  single  or  successive  ranges, 
according  to  the  principles  of  volley  fire. 

Zone  Fire  is  adapted  especially  to  the  sudden  attack  of 
troops  moving  or  liable  to  move.  The  special  characteristic 
of  this  method  of  fire  is  that  it  provides  for  searching  a deep 
area  with  the  utmost  rapidity,  and  thus  of  striking  the  enemy 
before  he  can  escape  from  that  area.  IT  IS  USED  ONLY 
FOR  THE  ATTACK  OF  IMPORTANT  BODIES  OF 
TROOPS  WHO  MUST  BE  STRUCK  AT  ONCE,  IF  AT 
ALL. 

A 200-yard  bracket  is  sought,  and  the  rafale  is  usually 
commenced  at  a range  100  yards  less  than  the  short  limit  of 
the  bracket.  Great  density  of  fire  is  thus  obtained  over  the 
full  depth  of  the  bracket. 

Fire  at  will  is  employed  solely  for  the  close  defense  of  the 
guns  from  hostile  attack.  If  the  distant  approach  of  the  enemy 
is  seen,  then  he  is  met  by  volleys,  the  range  being  successively 
decreased  in  accordance  with  his  rate  of  advance  and  the  fire 
being  held  under  rigid  control  until  the  last  moment;  but  when 
it  is  seen  that  a rush  for  the  guns  is  imminent,  fire  at  will 
should  be  ordered. 

Against  infantry  in  position  and  more  or  less  protected  by 
entrenchments  the  fire  should  be  carefully  adjusted.  As  our  in- 
fantry advances  to  the  attack  the  intensity  of  the  fire  should  be 
regulated  to  suit  the  necessities  of  the  case,  being  slow  or  ceas- 


160 


GUNNERY 


ing  entirely  while  the  enemy  is  concealed  or  inactive,  rising  to 
great  intensity  when  the  crises  of  the  action  develop  and  the 
enemy  exposes  himself  to  meet  them.  Continuous  fire  is 
indicated  for  the  ordinary  phases  of  the  action,  volleys  for 
the  crises,  the  object  being  to  assist  our  own  infantry;  by  inflict- 
ing as  much  damage  as  possible  upon  the  enemy;  by  destroy- 
ing his  morale;  by  forcing  him  to  keep  under  cover;  and  by 
preventing  effective  fire  upon  his  part. 

It  is  obviously  advantageous  to  employ  direct  fire  in  repel- 
ling an  infantry  attack,  certainly  in  its  final  stages.  This  will 
be  quite  impossible,  however,  in  many  cases,  if  the  hostile 
artillery  is  superior.  If  such  an  attack  is  foreseen,  the  guns 
to  be  employed  to  repel  it  should  be  well  placed  and  thor- 
oughly masked  in  advance,  otherwise  their  fire  will  be  silenced, 
whereas  if  their  position  is  not  disclosed  they  will  be  able  to 
play  upon  the  advancing  infantry  while  the  hostile  artillery 
is  searching  for  their  position.  The  final  stages  of  an  infantry 
attack  are  usually  of  such  short  duration  that  it  will  either  be 
repulsed  or  succeed  before  much  searching  can  be  done  by 
the  enemy  in  the  endeavor  to  locate  the  exact  position  of  the 
guns. 

It  was  frequently  found  impossible  in  Manchuria  to  employ 
indirect  fire  against  the  rapid  advance  of  attacking  infantr}'- 
with  any  degree  of  effect.  Very  often  the  Japanese  reached 
the  Russian  trenches  before  the  guns  of  the  latter  could  open 
upon  them  from  an  indirect  position.  Hence  the  Japanese 
claimed  that  direct  fire  should  be  used  to  repel  attack  and 
indirect  fire  in  the  preparation  for  an  attack. 

Against  artillery  in  position  the  first  object  is  to  gain  the 
ascendancy  over  it  by  inflicting  as  much  damage  as  possible 
upon  the  personnel.  Immediately  effective  fire  is  particu- 
larly demanded  if  the  enemy  can  be  attacked  at  a disadvan- 
tage, as,  for  example,  while  limbering,  or  unlimbering.  Obtain- 
ing a bracket  as  small  as  possible,  searching  the  depth  of  the 
bracket,  carefully  observing  the  fire  and  securing  as  prompt!}’- 


FIRE  AND  FIRE  DATA 


161 


as  possible  an  accurate  adjustment  are  the  means  to  be 
ordinarily  employed  in  attacking  the  personnel. 

Due  to  the  difficulty,  however,  of  reaching  effectively  the 
personnel  of  batteries  provided  with  shields  and  posted  in 
masked  or  semi-masked  positions,  the  struggle  between  evenly 
matched  artilleries  will  often  be  long  drawn  out.  If  the  ene- 
my’s artillery  is  temporarily  overmatched,  it  may  suspend  its 
fire  and  shelter  its  personnel ; but  it  must  be  expected  to  renew 
the  struggle  as  soon  as  the  pressure  upon  it  is  relieved.  The 
aim  must  be  to  gain  the  superiority  of  fire  by  suitable  concen- 
trations of  effort  on  the  part  of  our  own  artillery;  the  oppor- 
tunity may  then  be  gained  to  destroy  the  enemy’s  material  by 
well-adjusted  shell  fire. 

A slowly  moving  target  such  as  infantry,  or  mounted  troops 
impeded  in  their  march,  may  be  quickly  bracketed  by  salvos 
and  then  attacked  by  searching  fire. 

Infantry  in  march  formation  may  be  thus  attacked,  but 
immediate  deployment  on  their  part  is  to  be  anticipated,  and 
the  officer  conducting  the  fire  should  be  prepared  to  reach 
them,  probably  behind  cover,  with  a well-distributed  fire. 

Infantry  moving  to  attack  in  deployed  lines  or  in  line  of 
small  columns  may  be  met  by  volleys  successivly  reduced  in 
range  as  the  infantry  approaches.  If  their  formation  is  in 
line  of  small  columns  the  fire  should  be  distributed  so  that  a 
piece  or  platoon  may  bear  upon  each  of  the  small  columns. 

At  close  ranges  infantry  will  probably  endeavor  to  advance 
by  successive  rushes  from  cover  to  cover.  Such  rushes  may 
be  met  by  volleys  previously  prepared  for  upon  selected  posi- 
tions, evidently  in  the  immediate  path  of  the  enemy.  If  the 
positions  occupied  by  important  bodies  of  the  enemy  during 
the  intervals  of  advance  are  well  defined,  accurately  adjusted 
fire  may  be  brought  to  bear  upon  such  positions,  and  the 
ground  between  successive  positions  may  be  covered  by 
searching  fire  when  important  movements  of  the  enemy  from 
one  position  to  another  are  attempted. 


162 


GUNNERY 


In  the  case  of  a rapidly  moving  target,  if  the  target  is  moving 
at  right  angles  or  obliquely  to  the  line  of  fire,  it  is  ordinarily 
best  to  adjust  the  fire  upon  some  position  in  the  path  of  the 
target  and  ahead  of  its  movement  and  open  with  volleys  or 
with  zone  fire  as  it  approaches  the  position  selected.  If  the 
target  is  moving  parallel  to  the  line  of  fire,  or  nearly  so,  the 
target  may  be  bracketed  and  volley  fire  opened  at  that  limit 
of  the  bracket  toward  which  the  target  is  moving,  or  at  a lesser 
or  greater  range,  the  object  being  to  bring  fire  to  bear  upon  a 
point  in  advance  of  the  movement  of  the  target  and  to  con- 
tinue the  fire  until  the  target  has  passed  through  it.  A target 
having  been  once  brought  under  effective  fire,  its  subsequent 
movements  may  be  followed  by  volleys  varying  in  range  and 
direction,  according  to  the  rate  and  direction  of  march  of  the 
target. 

Designation  of  Objectives. — Targets  and  aiming  points 
must  be  designated  in  a concise  and  unmistakable  manner. 
Officers  must  exercise  themselves  in  describing  objectives  of 
all  kinds,  in  all  available  forms  of  terrain,  and  must  accustom 
those  under  them  to  the  terms  and  methods  employed  in  the 
description.  Practice  of  this  character  should  habitually 
form  a part  of  firing  instruction,  and  should  also  be  included 
in  the  instruction  of  scouts,  agents,  and  range  finders. 

If  the  targets  are  distinct  and  clearly  defined,  they  may  be 
designated  by  name,  as,  for  example,  “The  battery  on  hill 
1,240,”  “Cavalry  to  the  right  front,”  etc.  But  if  the  target  is 
indistinct  and  poorly  defined,  or  if  it  is  masked,  then  each  unit 
may  be  assigned  so  many  mils  of  a given  front  to  attack. 

In  designating  objectives  of  any  kind  (targets,  aiming 
points,  registration  marks,  etc.)  the  following  procedure  is 
appropriate,  especially  when  the  objective  is  not  conspicuous 
nor  readily  recognized: 

Define  the  relative  position  of  the  objective  and  its  char- 
acteristics. The  relative  position  is  fixed  by  giving  the  approx- 
imate direction  and  distance  of  the  objective  and  its  situation 


FIRE  AND  FIRE  DATA 


163 


with  respect  to  prominent  features  of  the  landscape.  The 
characteristics  usually  important  are  the  nature  of  the  object, 
its  shape  and  color. 

If  the  objective  is  in  itself  inconspicuous,  then  it  is  usually 
best  to  first  designate  the  most  prominent  object  in  its  general 
direction,  give  the  angular  distance  between  this  auxiliary 
objective  and  the  real  objective,  and  then  describe  the  latter 
as  before. 

The  usual  method  of  procedure  is  as  follows: — 

1.  Indicate  the  general  direction  of  the  objective. 

2.  Designate  the  most  prominent  object  in  the  zone  indi- 
cated. 

3.  State  the  angular  distance  from  this  auxiliary  object 
to  the  objective. 

4.  Designate  the  objective. 

Thus: 

1.  To  our  right  front. 

2.  At  3,000  yards  a large  stone  house,  square,  two-storied, 
with  a cupola  on  top. 

3.  500  mils  to  the  right  of  the  cupola. 

4.  At  2,500  yards  a battery  of  artillery  in  position  in  rear 
of  the  large  orchard. 

Or : — 

1.  To  the  left  rear. 

2.  At  4,000  yards  a line  of  hills  with  three  plainly  marked 
and  well-wooded  valleys. 

3.  350  mils  to  the  left  of  the  left  valley. 

4.  On  the  sky  line  of  the  hills,  a lone  tree,  low  and  bushy. 

Or: 

1.  Straight  to  the  front. 

2.  At  3,500  yards  a farmhouse  in  a grove  of  trees  on  a 
ridge. 

3.  Commencing  at  500  mils  from  the  left-hand  tree  of  the 
grove. 

4.  Cover  100  mils  of  the  crest  line. 


164 


GUNNERY 


Targets  and  aiming  points  are  preferably  designated  by 
word  of  mouth  and  to  a person  standing  near  by.  On  the 
occupation  of  a position  the  aiming  point  and  the  expected 
targets  should,  as  far  as  practicable,  be  thus  pointed  out  to 
the  officer  conunanding  the  guns. 

If  it  is  necessary  to  send  this  information  to  a person  at  a 
distance,  it  is  important  to  remember  that  objects  often  pre- 
sent very  different  appearances  if  viewed  from  widely  separated 
positions.  For  this  reason  it  is  desirable  to  select  as  aiming 
points  objects  having  a uniform  outline,  and  hence  presenting 
the  same  appearance  from  whatever  angle  they  are  viewed. 
The  information  is  transmitted  by  couriers  or  telephone.  If 
a courier  is  used,  he  is  required  to  keep  the  objective  in  view  as 
much  as  possible  while  passing  from  one  station  to  the  other. 

The  designation  of  objectives  may  be  greatly  facilitated  by 
causing  a panorama  sketch  of  the  terrain  to  be  prepared  and 
copies  to  be  furnished  the  different  subordinate  commanders 
concerned.  On  such  a sketch  important  landmarks  and  mili- 
tary objectives  should  be  named  or  numbered,  so  that  they 
may  be  readily  referred  to. 

Observing  the  Terrain;  Sectors  of  Observation;  Forming 
the  Sheaf ; Preparation  for  Firing. — In  preparation  for  definite 
and  imminent  phases  of  an  action,  certain  bodies  of  artillery 
may  be  ordered  to  observe  the  enemy  in  designated  portions 
of  the  terrain  and  be  ready  to  bring  him  under  immediately 
effective  fire. 

If  possible,  the  position  of  the  enemy  is  clearly  pointed  out; 
but  if  his  exact  position  within  a certain  area  has  not  been 
determined  the  area  may  be  divided  up  into  sectors  and  a 
sector  assigned  to  each  important  group  of  artillery.  In  the 
former  case  the  firing  data  are  determined  for  the  known  posi- 
tion of  the  enemy;  in  the  latter  case,  for  prominent  features 
of  the  terrain  within  the  sector  assigned. 

With  a view  to  gaining  readiness  for  instant  action,  the 
guns  may  be  laid  upon  the  target  or  upon  some  selected  feature 


FIRE  AND  FIRE  DATA 


165 


of  the  terrain  and  the  sheaf  formed  so  as  to  provide  for  the 
desired  distribution. 

To  form  the  sheaf,  an  aiming  point  is  selected,  a deflection 
is  given  the  right  piece  which  will  cause  it  to  be  directed  upon 
the  right  section  of  the  target,  or  upon  the  registration  mark, 
and  a deflection  difference  is  employed  which  will  suffice  to 
distribute  the  fire  over  the  known  or  expected  front. 

If  the  position  of  the  enemy  is  known  and  all  necessary  data 
have  been  obtained,  the  pieces  may  be  at  once  loaded. 

If  the  exact  position  in  which  the  enemy  will  appear  is  not 
known,  then  on  his  appearance  the  necessary  corrections  in 
range  and  direction  must  be  quickly  estimated  (or  measured) 
and  set  off.  The  correction  in  range  is  obtained  by  estimating 
the  target’s  distance  from  the  selected  registration  marks; 
the  correction  in  deflection  by  measuring,  by  means  of  hand- 
breadths  or  the  B.  C.  ruler,  the  angle  from  the  registration 
mark  to  the  section  of  the  target  which  is  to  be  attacked  by 
the  directing  piece.  The  circumstances  of  the  case  must 
decide  whether  the  pieces  are  loaded  before  the  target  appears. 

At  a mean  range  (about  3,000  yards)  a battery  may  be 
expected  to  cover  effectively  a front  of  about  30  mils  if  parallel 
&e  is  used. 

The  initial  opening  of  the  sheaf  depends  upon  the  nature 
of  the  expected  target  and  the  circumstances  of  the  action. 
Thus,  if  the  enemy’s  artillery  is  the  expected  target  a parallel 
formation  of  the  sheaf  may  be  preferable,  while  if  lines  of 
infantry  are  to  be  attacked  a more  open  formation  may  be 
appropriate. 

If,  in  order  to  assist  our  own  infantry,  the  artillery  is  called 
upon  to  repress  the  activity  of  a long  line  of  hostile  infantry 
in  position,  each  battery  may  be  required  to  act  over  a wide 
front.  Good  judgment  and  great  versatility  in  the  employ- 
ment of  fire  are  called  for  under  such  circumstances,  in  order 
that  the  desired  results  may  be  obtained  without  undue  expend- 
iture of  ammunition  in  the  earlier  phases  of  the  attack. 


166 


GUNNERY 


Means  may  be  employed  to  keep  the  entire  hostile  line  under 
the  menace  of  fire,  single  guns  being  freely  used  to  repress 
special  activity  of  the  enemy  in  the  sections  assigned  to  such 
guns. 

Registration  of  Fire. — Artillery  already  in  position  may 
take  advantage  of  lulls  in  the  progress  of  an  action  to  register 
its  fire  upon  positions  in  which  an  enemy  is  known  to  be  or  in 
which  he  is  expected  to  appear.  The  nature  and  circumstances 
of  the  action  determine  the  relative  importance,  on  the  one 
hand,  of  securing  this  information,  and,  on  the  other,  of  keep- 
ing concealed  the  position  of  our  own  artillery. 

The  purposes  of  fire  for  registration  are: 

(a)  To  determine  the  firing  for  reaching  certain  prominent 
features  of  the  terrain,  such  as  crests,  edges  of  forests,  villages 
or  cultivated  fields,  houses,  etc. 

(b)  To  discover  by  actual  fire  the  accidents  of  the  ground 
which  might  conceal  the  enemy  or  hide  the  points  of  burst  of 
our  projectile. 

(c)  To  thus  gain  the  ability  to  open  immediately  effective 
fire  upon  a target  appearing  at  or  near  these  prominent  fea- 
tures of  the  terrain. 

Registration  of  fire  is  especially  appropriate  for  artillery  to 
which  definite  sectors  of  observation  have  been  assigned,  as 
the  necessary  firing  data  may  thus  be  most  readily  obtained. 

If  the  position  of  the  enemy  wdthin  the  sector  is  definitely 
known — as,  for  example,  that  he  is  behind  a certain  crest  or 
in  the  edge  of  a certain  piece  of  woods — the  fire  is  directed 
upon  some  prominent  landmark  at  or  near  the  enemy’s  posi- 
tion as  the  registration  mark,  and  the  data  thus  secured  in 
advance  for  opening  prompt  and  effective  fire. 

If,  however,  the  enemy’s  position  within  the  sector  has  not 
been  located,  the  artillery  commander  proceeds  in  a sj^stematic 
way  to  secure  the  data  which  will  enable  him  to  reach  promptly 
and  effectively  any  part  of  the  sector.  He  studies  the  terrain, 
decides  upon  the  limits  in  width  and  depth  of  the  area  to  be 


FIRE  AND  FIRE  DATA 


1167 


registered,  notes  the  specially  prominent  features  of  the  ter- 
rain within  these  limits,  and  by  actual  firing  directed  upon  these 
natural  features  secures  the  data  which  will  enable  him  to 
reach  promptly  any  target  appearing  in  their  vicinity. 

Fire  Data. — Fire  is  classified  as  direct  and  indirect  accord- 
ing to  the  method  employed  in  laying  the  piece  and  sights. 

When  the  target  is  clearly  visible  through  the  sights  the 
method  of  sighting  the  piece  is  direct.  This  method  is  called 
direct  laying. 

When  an  obstacle  intervenes  between  the  sights  and  the 
target,  such  as  a hillside,  the  sighting  of  the  piece  must  be 
indirectly  done,  and  this  method  is  called  indirect  laying.  The 
intervening  obstacle  is  called  a mask,  which  will  be  discussed 
later. 

Whichever  method  is  employed,  it  is  necessary: 

1.  To  so  direct  the  axis  of  the  gun  that  the  projectile  will 
pass  in  the  direction  of  the  target.  (Deflection.) 

2.  To  so  elevate  the  axis  that  the  projectile  will  reach  the 
target.  (Range.) 

3.  To  so  regulate  this  elevation  that  the  trajectors  will 
pass  through  the  target  whether  above  or  below  the  piece. 
(Angle  of  sight.) 

4.  To  cause  the  projectile  (if  shrapnel  is  used)  to  burst 
where  it  will  give  the  maximum  effect.  (Corrector.) 

For  direct  fire,  each  gunner  sets  his  sights  at  the  prescribed 
elevation  and  deflection,  and  aims  his  gun  as  he  would  a rifle. 
The  only  other  instrument  the  use  of  which  is  involved  is  the 
fuse  setter  in  case  of  time  shrapnel  fire.  The  firing  data  for 
direct  fire,  then,  are: 

1.  Deflection.  (Wind  and  drift.) 

2.  Fuse  setting. 

3.  Range. 

Indirect  fire  involves  more  details  which  appear  at  first 
sight  more  troublesome,  principally  by  reason  of  the  fact  that 
all  angular  measurements  are  computed  in  mils,  a technical 


168 


GUNNERY 


unit  which  is  really  a definite  fraction  of  a degree.  Before 
going  into  the  subject  of  Indirect  Laying,  it  is  essential  that 
the  mil  be  thoroughly  understood. 

A mil  is  an  angle.  It  corresponds  in  form  to  a degree  and 
not  to  lineal  measures  as  feet,  yards,  etc.  It  is  that  angle 
which  a tangent  equal  to  1/1,000  of  a radius  will  intercept  at 
the  center  of  a circle. 


t 


A tangent  is  a straight  line  perpendicular  to  the  radius  at 
its  intersection  with  the  circumference  of  the  circle.  (Figure  2.) 

Now  it  has  been  found  that  in  any  circle  there  are  approxi- 
mately 6,400  mils. 

Since  there  are  360°  in  a circle: 

Circle  360°  = 6,400  mils. 

Straight  angle  180°  = 3,200  mils. 

Right  angle  90°  = 1,600  mils, 

45°  = 800  mfis. 

All  calculations,  as  has  been  said,  must  from  now  on  be 
made  in  mils.  It  is  readily  seen  how  adaptable  the  unit  is 
both  to  horizontal  and  vertical  measurements,  for  if  a mil  is 
that  angle  which  is  intercepted  at  the  center  by  a tangent 
equal  to  1/1,000  of  the  radius,  so  the  tangent  which  a mil  will 
subtend  at  any  range  is  equal  to  1/1,000  of  that  range  as  illus- 


FIRE  AND  FIRE  DATA 


169 


trated  in  the  figure.  At  any  range  the  front  of  the  target  is 
taken  as  the  tangent  to  a circle  of  which  the  range  is  the 
radius. 

In  order  to  determine,  then,  what  number  of  yards  a mil 
subtends  at  a given  range,  it  is  only  necessary  to  divide  the 
range  by  1,000.  (Figure  3.) 


3.5  yds. 


Thus  1 mil  subtends  1 yd.  at  R 1,000, 

10  mils  subtend  10  yds.  at  R 1,000, 

1 mil  subtends  2 yds.  at  R 2,000, 

20  mils  subtend  40  yds.  at  R 2,000, 

50  mils  subtend  250  yds.  at  R 5,000. 

Before  proceeding  further,  it  must  be  understood  that  the 
sum  of  the  angles  of  any  triangle  = 180°. 

But  180°  = 3,200  mils. 

. * . The  sum  of  the  angles  of  a triangle  = 3,200  mils. 

Also  that  vertical  angles  are  equal.  (Figure  4.) 


a and  Ui  are  vertical  angles  and  so  also  h and  hi. 


170 


GUNNERY 


In  Figure  5,  x + 90°  + a = xi  + 90°  + ai 

a = tti  (vertical  angles) 
right  angles  are  also  equal. 

X = Xi 


Fig.  5. 

It  should  also  be  understood  that  the  square  of  the  hypot- 
enuse is  equal  to  the  sum  of  the  squares  of  the  other  two  sides 
of  a triangle.  The  hypotenuse  is  the  side  opposite  the  right 
angle.  (Figure  6.) 


= x^ 

^2  = _ y1 

— x^ 

This  rule  is  called  the  Pons  Asinorum;  so  named  from  the 
similarity  of  the  geometrical  figure  to  a bridge,  and  the  diffi- 
culty many  beginners  experience  in  getting  over  it;  hence  pons 
asinorum — the  asses’  bridge.  And  here  it  may  be  said  that 
it  would  be  foolish  indeed  to  attempt  to  cross  to  the  next 
chapter  without  a thorough  grasp  of  the  meaning  of  the  term 
mil.  It  is  easy  to  remember  if  we  recall  its  derivation  from  the 
Latin  word  mille,  meaning  thousand. 


CHAPTER  II 


INDIRECT  FIRE  AND  DEFLECTION 

Indirect  fire  involves  many  details  which  only  constant 
practice  and  study  will  master.  It  is  possible  for  a gunner  to 
deliver  an  effective  du'ect  fire  without  much  knowledge  of 
gunnery,  for  he  may  be  as  skillful  in  estimating  the  range  and 
in  the  mechanical  adjustment  of  sights  and  fuse  setter  as  the 
most  learned  artillerist.  Before  proficiency  and  effectiveness 
may  be  attained  in  indirect  fire,  however,  it  is  absolutely 
necessary  that  a complete  knowledge  of  the  subject  be  had. 
In  fact,  it  would  be  impossible  to  even  practice  indirect 
firing  without  understanding  the  underlying  principles  of  the 
method. 

In  indirect  fire,  it  is  contemplated  that  an  obstacle  inter- 
venes between  the  guns  and  the  target,  the  obstacle  serving 
to  mask  the  guns  from  the  view  of  the  enemy. 

If  the  guns  are  behind  such  an  obstacle  with  respect  to  the 
target,  it  is  obvious  that  the  target  is  not  discernible  from  the 
guns.  It  is,  therefore,  necessary  for  the  battery  commander 
to  seek  a position  from  which  he  can  see  both  the  target  and 
the  guns  and  rapidly  communicate  with  the  men  at  the  latter. 
This  point  of  observation  should  preferably  be  on  a flank  of 
the  line  of  guns,  or  directly  in  rear  of  and  above  them.  It  is 
called  the  battery  commander’s  station. 

Now  it  is  plain  that  if  the  battery  commander,  from  his 
observing  station,  B,  Figure  1,  sights  his  instrument  at  some 
point,  P,  visible  through  the  telescopic  sights  of  the  guns,  and 
then  revolves  his  telescope  until  the  target,  T,  is  picked  up, 

171 


172 


GUNNERY 


that  the  horizontal  angle  PBT  fixes  the  direction  of  T with 
respect  to  B.  This  horizontal  angle  or  a is  called  the 
azimuth  of  the  target  and  the  point  P,  visible  from  the  guns, 
is  called  the  aiming  point.  This  angle  may  be  measured  by 
the  battery  commander’s  telescope  (see  page  109,  Hand- 
book of  the  3-inch  Field  Artillery  Material,  1908),  by  the 
battery  commander’s  ruler,  (ibid.,  114)  or  by  the  hand. 
(The  last  two  methods  will  be  subsequently  explained  in  this 
chapter.) 

Aiming  Point. — Before  proceeding  further,  it  is  well  to 
dwell  upon  the  subject  of  “Aiming  Point.”  (Drill  Regula- 
tions, 1908,  Paragraphs  444,  445.) 

When  indirect  laying  is  to  be  employed,  the  selection  of  a 
suitable  aiming  point  calls  for  special  attention.  The  aiming 
point  should  be: 

1.  Surely  visible  from  the  emplacement  of  each  gun; 

2.  Distinctive  and  easily  picked  out; 

3.  At  a considerable  distance  from  the  guns;  and 

4.  Preferably  near  the  normal  to  the  line  of  guns. 

If  any  doubt  whatever  exists  as  to  the  visibility  of  the  aim- 
ing point,  it  is  always  best,  before  the  guns  come  up,  to  go  to 
the  point  where  each  gun  is  to  be  placed  and  make  sure  that 
the  aiming  point  will  be  visible  through  the  sights  from  that 
point. 

Some  object  which  quickly  attracts  the  eye  should  be 
selected;  and,  if  possible,  it  should  be  the  only  object  of  its 
kind  in  the  vicinity,  so  that  doubt,  hesitation,  and  mistakes 
may  not  arise,  either  in  the  designation  of  the  aiming  point 
or  in  finding  it  quickly  after  looking  away. 

A distant  aiming  point  is  preferable,  for  the  more  the  aim- 
ing point  is  removed  from  the  guns  the  more  are  errors  in  cal- 
culation of  parallax  minimized.  But  it  is  not  desuable  to 
take  inconspicuous  aiming  points  or  those  at  distances  so  great 
as  not  to  be  readily  determinable.  Usually  points  not  less 


INDIRECT  FIRE  AND  DEFLECTION 


173 


than  2,000  and  not  more  than  6,000  yards  distant  will  be  found 
most  suitable. 

A point  in  rear  or  in  front  of  the  guns  and  near  the  normal 
to  their  front  is  always  to  be  preferred,  provided  it  is  at  least 
1,000  yards  distant.  If  the  aiming  point  must  be  closer  than 
1,000  yards,  then  it  is  best  to  have  it  on  the  flank. 

If  the  distant  aiming  point  is  apt  to  be  obscured  by  mist  or 
smoke,  then  a secondary  aiming  point  should  be  provided  for. 
A stake  may  be  put  up  for  the  purpose.  The  guns  having 
been  oriented  on  the  target  by  means  of  the  distant  aiming 
point,  the  sights  may,  when  necessary,  be  turned  upon  the 
new  aiming  point  and  the  latter  used  in  subsequent  fire. 


Calculation  of  Formula. — If  the  right  gun.  Figure  1,  were 
aimed  at  P and  then  turned  through  an  angle  equal  to  a,  the 
final  direction  of  its  line  of  fire  would  not  pass  through  T, 
but  through  Ti,  since  the  angle  z is  equal  to  angle  a. 

The  necessary  correction  may  be  arrived  at  in  the  follow- 
ing manner: 

In  Figure  2 the  angle  D is  the  angle  through  which  the  axis 
of  the  gun  must  be  turned  from  the  aiming  point  to  give  the 
direction  of  T or  the  target,  and  is  called  the  angle  of  deflec- 
tion or  merely  the  deflection  of  the  sight  piece. 

In  the  two  triangles  BPX  and  GTX  the  angles  at  X are 


174 


GUNNERY 


evidently  equal.  We  also  know  that  B+P+X  = 3,200  mils 
and  G-}-T-{-X  = 3,200  mils. 

.-.B+P+X  = G+T+X 
Subtracting  X from  both  sides — 

B+P-G+T 

G=B+P-T 

G-B+(P-T) 

G = D B = A .-.  D = A+(P— T) 

Now  it  will  be  remembered  that  angles  are  measured  in 
mils  and  the  value  of  P and  T may  be  determined,  knowing 


T 


the  range,  the  distance  to  the  aiming  point,  and  the  dis- 
tance from  the  guns  to  the  observing  station  or  GB  in  the 
figure. 

Thus  if  R is  3,000  yds.  a mil  subtends  3 yds.,  and  if  GB  is 
60  yds.,  it  must  be  subtended  by  an  angle  of  20  mils,  hence: 
T = 20. 

If  BP  is  2,000  yds.  a mil  subtends  2 yds.,  and  if  GB  is  60 
yds.  it  must  be  subtended  by  an  angle  of  30  mils,  hence: 
P = 30. 


INDIRECT  FIRE  AND  DEFLECTION 


175 


Now  if  the  azimuth  or  a is  1,600  mils  as  measured  by 
the  telescope,  we  have; 

D = 1600+30—20  = 1610. 

This  is  the  principle  upon  which  deflection  is  determined 
by  the  parallax  method  prescribed  in  the  Drill  Regulations. 
The  easiest  way  to  grasp  the  parallax  method  is  first  to 


understand  the  meaning  of  the  work  parallax.  This  word  is 
derived  from  the  Greek  word  parallaxis,  from  para,  beyond, 
and  allassein,  to  change. 

The  parallax  then  is  the  apparent  change  of  position  of  an 
object  when  viewed  from  different  places. 

An  observer  at  A,  Figure  4,  sees  an  object  at  B in  a line  with 
C,  but  when  he  moves  to  the  positions  D and 
F it  appears  in  line  with  E and  G respectively. 

This  apparent  alteration  of  position,  as  if  the 
object  were  retreating  as  the  observer  ad- 
vances, is  called  parallax.  Parallax  is  measured 
by  the  angle  at  the  object.  Thus  the  parallax 
of  B,  with  respect  to  positions  A and  D,  is 
the  angle  ABD,  which,  of  course,  is  equal  to 
the  vertical  angle  EBC. 

Parallax  may  again  be  illustrated  by 
Figure  5. 

Suppose  A and  B are  your  eyes  and  0 an 
object.  If  you  close  the  right  eye  your  line 
of  sight  is  BO,  and  if  you  close  the  left  eye  your  line  of 
sight  is  AO. 


Fig.  5. 


176 


GUNNERY 


The  angle  BOA  is  the  optical  or  binocular  parallax.  It 
is  readily  seen  that  as  the  object  recedes  the  angle  de- 
creases. 

Optical  parallax  can  be  easily  tested  in  the  following 
manner. 

Place  a pencil  on  the  floor  at  the  left  edge  of  a door  frame 
so  that  it  can  just  be  seen  with  the  right  eye  as  you  look  through 
the  door  opening.  Close  the  right  eye  and  the  pencil  will  dis- 
appear. This  is  just  what  happens  when  the  battery  com- 
mander leaves  his  station  for  the  guns.  The  target  disappears. 

From  his  station  it  is  necessary  for  him  to 
calculate  firing  data  with  his  open  eye  for 
the  blind  eye  of  the  battery. 

For  the  sake  of  convenience  a handy 
rule  has  been  worked  out,  which,  based 
upon  the  foregoing  principle,  shortens  the 
calculation  of  deflection.  The  parallaxes 
of  the  angles  P and  T have  been  calcu- 
lated for  every  range  with  a base  of  20 
yds.  or  1 platoon  front,  thus: 

If  range  is  3,000  yds.  each  mil  has  a 
lineal  value  of  3 yds.  and  the  angle  T 
(Figure  6)  must  be  6f  mils  to  subtend  the  base  of  20  yds.  The 
nearest  whole  number  is  taken,  so  that  in  this  case  the  parallax 
of  T is  7.  In  other  words,  to  determine  the  parallax  of  any 
angle  divide  20  yds,  by  1/1,000  of  the  range;  thus: 

T - 20/3  = 6|  = 7 
P = 20/2  = 10 

But  in  Figure  6 the  base  is  100  yds.  and  angles  at  P and  T 
are  five  times  larger  than  they  would  be  for  a base  of  20  yds. 
Therefore,  they  are:  5X7  = 35  and  5X10=  50. 

We  found  that: 


D = a-fP-T 
D = a+(P-T) 


INDIRECT  FIRE  AND  DEFLECTION 


177 


If  we  take  the  value  of  (P — T)  for  a 20-yd.  base  (10 — 7), 
and  multiply  the  bracket  by  the  number  of  times  20  goes  into 

the  base,  or  = 5,  we  have  the  actual  value  of  (P — T) : a 
20 

is  measured  with  the  instrument;  therefore: 

D-a+5  (10—7) 

The  rule  is  generally  stated: 

D = a+n  (P — T) 

n is  the  number  of  platoon  fronts  in  the  base. 

If  the  observing  station  is  on  the  right  of  the  guns  n is 
always  positive  or  plus  (+) ; if  on  the  left  n is  always  negative 


or  minus  ( — ).  And  so  if  the  aiming  point  is  in  front  of  the 
prolongation  of  the  line  of  guns  P is  positive  (+);  and  if  in 


178 


GUNNERY 


rear  it  is  negative  ( — ).  In  all  these  calculations  it  is  assumed 
that  the  base  is  so  small  compared  to  the  range  and  the  dis- 
tance to  the  aiming  point  that  GT  is  equal  to  BT,  and  that  BP 
is  equal  to  GT.  Of  course,  the  base  in  the  figme  is  largely- 
exaggerated. 

Now  let  us  calculate  the  deflection  when  the  aiming  point 
is  in  the  rear  and  the  observing  station  is  on  the  right  (Figure  7). 

D==a-fn  (P — T) 

If  the  base  is  200  yds.  n = 5.  Since  the  station  is 

• 20  ^ 

on  the  right  n is  positive. 


T 


20 

P = — = 7 (Negative  because  in  rear.) 

(P-T)=(-7-5)  = (-12) 
or  n (P-T)=5(-12)  = -60 


A is  measured  with  the  instrument  and  found  to  be  2,600 
mils. 

.-.  D = 2,600 -|-5(- 12)  =2,600 -60  = 2,540. 

If  AP  is  in  rear  and  the  observing  station  is  on  the  left, 
the  result  is  different.  (Figure  8.) 

T^  — cl-\-71  (P — T) 

71  = 200/20=  —10.  (Since  station  is  on  the 
left  it  is  negative.) 

T = 20/4  = 5 P = 20/3=-7 

(P— T)  = (— 7— 5)=— 12 
n (P— T)=— 10(— 12) 

A is  measured  and  found  to  be  2,600  mils. 

D = 2,6004- (-10(- 12)) 

D = 2,600 -10(- 12) 

D = 2,600+120 
D = 2,720 

Now  it  will  be  observed  that  when  the  obser\ung  station 


INDIRECT  FIRE  AND  DEFLECTION 


179 


was  on  the  right  D was  less  than  A or  the  deflection  was  less 
than  the  azimuth ; and  when  the  observing  station  was  on  the 
left  D was  greater  than  A.  These  results  are  graphically 
illustrated  by  the  figures.  The  contained  angle  must  natur- 
ally be  the  larger. 

The  rule  of  the  Drill  Regulations  should  now  be  readily 
understood.  It  is: 

Rule  V.  The  deflection  of  the  right  piece  is  equal  to  the 
angle  from  the  aiming  point  to  the  target  (A), 
as  measured  at  the  observing  station,  increased 
algebraically  by  as  many  times  the  convergence 
difference  (P — T)  as  there  are  platoon  fronts  (n) 
in  the  interval  between  observation  station  and 
right  piece;  or 

D = A-fn  (P— T). 

So  far,  however,  we  have  only  calculated  the  deflection  of 
the  right  piece.  If  the  guns  are  20  yds.  apart  and  each  one  is 
laid  with  the  same  deflection,  it  is  obvious  that  there  would 


100  yds. 

B 


be  four  parallel  lines  of  fire,  the  right  one  only  passing  through 
the  target.  (Figure  9.) 

It  is  necessary,  therefore,  to  converge  G2,  G3,  and  G4  upon 

T. 


BGi  = n = 5. 


180 


GUNNERY 


If  the  pieces  are  20  yds.  apart: 

BG2  = n+l  = 6 
BG3=n+2  = 7 
BG4=w-1-3 =8 

Or  deflection  for  the  pieces  is 

DGi  = A+5(P-T) 

DG2-A+6(P-T) 

DG3  = A+7(P-T) 

DG4-A+8(P-T) 

Now  the  differences  between  the  deflection  of  Gi  and  the 
other  pieces  or  the  deflection  differences  (DD)  are: 

(G2)  A+5(P— T)— A+6(P— T)-1(P— T) 

(G3)  A+5(P— T)— A+7(P— T)  = 2(P— T) 

(G4)  A+5(P— T)— A+8(P— T)=3(P— T) 

Hence;  if  these  are  the  deflection  differences  between  the 
2d,  3d  and  4th  piece  and  the  right  or  1st  piece,  the  extent 


Fig.  10. 


any  piece  must  be  converged  is  equal  to  the  deflection  differ- 
ence of  the  1st  piece  or  (P — T)  multiplied  by  the  number  of 
platoon  fronts  from  the  right  piece. 

If  the  pieces  were  converged  upon  Ti  (Figure  10)  only  one 
point  of  a wide  front  would  be  subjected  to  fire.  If  the  pieces 
were  not  converged  still  only  a small  portion  of  the  front  would 


INDIRECT  FIRE  AND  DEFLECTION 


181 


be  affected  by  the  parallel  fire  of  the  guns.  The  natural  thing 
to  do,  therefore,  is  to  divide  the  entire  front  of  the  target  and 
give  each  piece  a fourth  to  fire  upon.  This  is  distributing  the 
fire.  In  order  to  distribute  the  fire  we  must  first  converge 
upon  Ti.  The  convergence  differences  are: 

CD  of  G2=  (P-T) 

CD  of  G3  = 2(P-T) 

CD  of  G4  = 3(P-T) 

Now  if  the  range  is  2,000  yds.  each  mil  subtends  2 yds.  If 
the  front  (F)  is  200  yds.  wide  J F = 50  yds.  50  yds.  would  be 
subtended  by  25  mils  at  the  gun  or  25  mils  would  have  to  be 
added  to  the  deflection  of  G2  to  throw  its  fire  \ of  the  front  to 
the  left  of  Ti. 

Now  then,  to  the  convergence  difference  of  each  piece  we 
must  add  J of  F multiplied  by  the  number  of  platoons  from 
the  right  gun.  Therefore, 

DD  for  G2=  (P-T)+iF; 

DD  for  G3  = 2(P-T)+2(iF)=2((P-T)+iF) 

DD  for  G4  = 3(P-T)+3(iF)=3((P-T)+iF) 


It  will  be  seen  that  adding  (P — T)  for  convergence  and 
(P — T)+iF  for  distribution  to  the  deflection  of  any  one  piece 
gives  the  deflection  of  the  next  piece. 


182 


GUNNERY 


The  convergence  difference  for  each  piece  then  is  as  fol- 
lows: 

(G2)  CD=  (P-T)  or  DD 

(G3)  CD  = 2(P-T)  or  2DD 

(G4)  CD  = 3(P-T)  or  3DD 

Now  let  us  consider  a target  with  a wide  front.  (Figure  11.) 

If  it  be  desired  to  converge,  and  (P — T)  = — 10 : 

D for  Gi  = 3,200; 

D for  G2  = 3,200-1- (-10)  =3,190 
D for  Gs  = 3,190-1- (-10)  =3,180 
D for  G4  = 3, 180-1- (-10)  =3, 170 

The  same  results  are  obtained  by  the  other  method,  viz. : 

D for  Gi  = 3,200 

D for  G2  = 3,200-1-  (-10)  =3,190 
D for  Gs  = 3,200-l-2(- 10)  =3,180 
D for  G4  = 3,200+3(- 10)  =3,170 

And  for  distribution  the  first  method  is: 

D for  Gi  = 3,200 

D for  G2  = 3,200-1- (-10) -1-25  = 3,215 
D for  Gs  = 3,215-1- (-10) -1-25  = 3,230 
D for  G4  = 3,230-1- (-10) +25  = 3,245 

And  by  the  other  method  the  same  result  is  obtained. 

D for  Gi  = 3,200 

D for  G2  = 3,200+  1((P-  T)  +|F)  = 3,200+ ( - 10)  +25  = 3215 
DforG3  = 3,200+2((P-T)+iF)=3,200+2((-10)+25)=3230 
D for  G4  = 3,200+3((P-T)  +iD  = 3,200 +3 ( ( - 10)  +25)  = 3245 

If  all  four  of  the  pieces  are  converged  upon  the  target  and 
it  be  desired  to  resume  parallel  fire,  the  deflection  difference 
is  equal  to  the  parallax  of  the  target.  (Figure  10.) 

The  desired  direction  for  G2  is  G2T  which  is  parallel  to 
GiTi  and  angle  Ti  or  the  necessary  deflection  for  the  line  of 


INDIRECT  FIRE  AND  DEFLECTION 


183 


fire  for  G2  is  equal  to  the  angle  T or  the  parallax  of  the  target. 
Therefore,  for  parallel  fire — 

DD  = P. 

Referring  to  Figure  11,  it  will  be  seen  that  with  shrapnel  fire 
a part  of  the  effect  of  the  right  gun  would  be  lost  if  Gi  were 
directed  straight  at  Ti  and  also  that  the  extreme  left  of  the 
front  would  be  uncovered.  This  is  provided  for  by  directing 
the  right  gun  about  10  yds.  within  the 
right  edge.  One  gun  can  only  cover  effect- 
ively about  20  yds.  of  front  so  that  if  the 
front  is  over  80  yds.  there  are  spaces  un- 
swept by  fire.  If  these  spaces  are  large 
they  may  be  covered  by  using  sweeping  fire. 

The  Drill  Regulations,  paragraph  437, 
tell  us  that,  when  the  observing  station  is 
in  advance  or  in  rear  of  the  line  of  guns, 
the  formula  D = A-f-n  (P — T)  is  only 
approximately  correct.  Major  McNair 
solves  the  problem  by  a method  he  calls 
the  fictitious  gun  method, 
which  is  as  follows  (Figure 
12): 

The  formula  D = A -f  n 
(P — T)  will  give  the  angle 
D for  the  right  gun,  Gi,  and 
Fig  12.  observing  station  at  B. 

So  would  the  formula  give 
the  angle  Di,  for  a gun  at  Gf  and  an  observing  station  at  Bi. 
It  is  manifest  that  Di  and  D are  not  equal. 

Draw  a line,  GfZ,  through  Gf  and  parallel  to  the  line  GiP. 
It  is  seen  that  angle  ZGfT  is  equal  to  angle  PGiT  or  D. 

The  angle  ZGfT  is  made  up  of  two  angles,  namely,  PGfT 
= Di  and  PGfZ.  Therefore  D is  greater  than  Di  by  the  angle 
PGfZ. 


H — h+Gi 


184 


GUNNERY 


Since  GfZ  and  GiP  are  parallel,  angle  PGfZ  is  equal  to 
angle  GiPGf.  But  angle  GiPGf  is  the  parallax  of  the  point 
P with  respect  to  the  line  GfGi. 

Suppose  the  angle  Ai  to  be  1,700  mils;  the  range  to  target 
3,300  yds.;  and  the  distance  to  P from  B,  1,000  yds.  ThenP 
= 0 and  T = 6 and  n = 6.  Appl3dng  the  formula: 

Di  = 1,700+6(0— 6)  = 1,664. 

But  we  have  seen  that  this  angle  is  too  small  by  the  parallax 
of  P times  the  number  of  platoon  fronts  in  GfGi  or  since  the 
parallax  of  P = 20  and  GfGi  = 8 platoon  fronts,  we  must  add 
8X20=160  mils  to  the  angle  given  by  the  formula  in  order  to 
be  nearly  correct. 

The  more  distant  P the  smaller  its  parallax,  and  if  very 
distant  8XP  would  be  so  small  as  to  be  negligible. 

Again,  if  the  aiming  point  had  been  nearly  in  rear  of  the 
guns,  its  parallax  with  respect  to  the  line  GfGi  would  have 
been  greatly  reduced  on  account  of  its  obliquity  to  that  line 
and  8XP  would  have  been  negligible. 

Therefore,  unless  aiming  points  are  quite  close  and  have 
considerable  obliquity,  the  correction  for  the  fictitious  gun 
need  not  be  made  as  the  parallax  method  is  only  approximate 
at  its  best. 

When  Aiming  Points  Are  Not  Available. — So  far,  in  dealing 
with  the  subject  of  deflection,  we  have  assumed  a suitable 
aiming  point  available.  Under  such  circumstances  the  cal- 
culation of  deflection  in  the  field  is  comparatively  simple  when 
once  the  underlying  principles  are  well  understood.  The  prac- 
tical difficulties  of  indirect  fire,  however,  lie  in  the  absence  of 
aiming  points  visible  from  all  the  guns  and  the  obser\dng 
station.  One  who  has  had  the  slightest  experience  in  the  field 
must  be  struck  by  the  difficulties  encountered  in  securing  such 
a point,  especially  in  a low  or  in  a close  country.  In  actual 
service  many  of  the  difficulties  encountered  at  drill  may  be 
obviated  by  the  free  use  of  the  axe. 


INDIRECT  FIRE  AND  DEFLECTION 


185 


If  an  aiming  point  visible  from  all  the  guns  and  from  the 
observing  station  can  not  be  found,  then  some  expedient  must 
be  devised  for  directing  the  guns  upon  their  targets.  The 
following  are  given  as  examples  of  such  expedients: 

Example  i. — To  Direct  a Piece  Upon  the  Target. — Suppose 
no  aiming  point  is  visible,  that  the  guns  are  in  position  behind 


J 

f / 
/ / 

// 

/ / 

/ 1 
/ / 

/ / 

/ / 

/ / 

/ / 

/ / 

// 

-j-az  -j-a2  - 

-0,1 

/ / 
fba  -^&2  • 

/ 

1 

Fig.  13. 

a mask,  and  it  be  desired  to  direct  one  of  the  pieces  upon  the 
target. 

Solution. — In  Figure  13,  let  T be  the  target,  G the  gun  to 
be  directed,  and  mm  the  ridge  of  the  intervening  mask. 

Let  a man  take  a position  as  at  ai  from  which  he  can  see 
the  target,  and  another  take  the  position  hi  from  which  he  can 
line  Ui  with  the  target.  The  gunner  directs  them  to  move  to 
successive  positions  as  ai  and  62,  as  and  63,  until  the  two  men 
give  the  proper  direction.  The  rear  man  must  always  keep 
the  front  one  in  line  with  the  target  and  the  gunner  causes  them 
both  to  move  until  &3  covers  as. 


186 


GUNNERY 


Example  2. — Use  of  a Directing  Piece. — The  guns  are  in  a 
depression  and  all  view  of  the  surrounding  country  is  cut  off. 
No  natural  aiming  points  are  visible. 

Solution. — First,  at  least  one  gun  must  be  directed  upon 
the  target.  If  the  battery  commander  can  look  over  the 
line  of  metal,  from  a tower,  or  a tree,  he  can  direct  a piece 
upon  its  appropriate  part  of  the  target  with  fair  accuracy. 
But  observing  towers  and  natural  points  of  vantage  are  not 
commonly  to  be  found  in  the  field,  and  more  often  some  such 


method  of  directing  a gun  as  the  one  described  in  Example  1 
must  be  relied  upon. 

Let  us  suppose,  in  Figure  14,  that  the  third  piece  has  been 
directed  upon  the  target  and  that  parallehsm  of  the  fines  of 
fire  of  all  the  guns  has  been  secured. 

Now  suppose  Gi  is  the  aiming  point  employed  by  Gs.  The 
deflection  for  G3  is  the  angle  dz.  But  if  the  sight  of  G3  is 
employed  by  G2  and  Gi  as  an  aiming  point,  the  deflection  of 
G2  and  Gi  for  parallel  fire  is  the  angle  do+3,200,  and  di+3,200 
respectively. 

But  ^2  and  di  both  equal  dz. 


INDIRECT  FIRE  AND  DEFLECTION 


187 


Therefore  the  formula  for  the  deflection  for  G2  is 
D2  = D3+3,200. 

And  the  formula  for  the  deflection  of  Gi  is 
Di  = D3+3,200. 

Therefore,  if  a directed  piece  be  used  as  an  aiming  point  the 
deflection  for  parallel  Are  for  all  the  pieces  to  the  right  thereof 
is  the  deflection  of  the  directed  piece +3,200. 

Now  consider  G4,  in  Figure  15. 


Suppose  G3  be  laid  on  Ts  with  the  sight  of  G4  as  an  aim- 
ing point.  The  deflection  of  G3  is  the  exterior  angle  at  G3, 
or  the  angle  c?3+ 3,200.  But  the  deflection  of  G4  for  parallel 
fire  if  G3  be  used  as  an  aiming  point  is  the  angle  di. 

'Di  = di^dz,  or 

ID4  = dz 

D3  = d3+3,200 

D3— 3,200  = ^3+3,200— 3,200 
D3— 3,200  = ^3 
dz  — D4 
.-.Ds— 3,200  = D4 


188 


GUNNERY 


Therefore,  if  the  sight  of  a directed  piece  be  employed  as  an 
aiming  point,  for  parallel  fire  the  deflection  of  all  pieces  to  the 
left  thereof  is  the  deflection  of  the  directed  piece — 3,200. 


The  formulae  having  been  deduced,  now  let  us  apply  them 
in  Figure  16. 

Suppose  Gs  directed  upon  the  target.  To  compute  deflec- 
tion for  the  other  pieces  proceed  as  follows: 

Cause  the  gunner  of  the  third  piece  to  turn  his  panoramic 
sight  upon  the  panoramic  sights  of  each  of  the  other  pieces 
in  turn  and  to  read  off  the  respective  angles. 

For  pieces  to  the  right  of  the  directed  piece  the  angle  is 
increased  by  3,200,  and  for  pieces  to  the  left  it  is  diminished  by 
3,200,  the  resultants  being  the  deflections  to  be  employed  for 
the  pieces  respectively,  the  panoramic  sight  of  the  directed 
piece  being  the  aiming  point  for  all  other  pieces. 

Obviously,  it  is  immaterial  which  piece  is  directed  upon  the 
target  to  start  with.  Naturally  the  one  which  can  be  directed 
with  the  greatest  facility  should  be  employed.  If  the  first 
piece  is  directed,  its  deflection  from  the  sights  of  the  other 
pieces  will  be  diminished  by  3,200  for  every  other  piece,  and 


INDIRECT  FIRE  AND  DEFLECTION 


189 


if  the  fourth  piece  is  directed  its  deflection  from  the  sights 
of  the  other  pieces  will  be  increased  by  3,200  for  every  other 
piece. 

Now  suppose  (Figme  17),  that  parallelism  of  fire  has  been 
secured  by  the  foregoing  method.  The  use  of  the  sight  of  the 
directed  piece,  as  an  aiming  point,  can  now  be  abandoned  and 


any  other  suitable  point  can  be  selected  by  the  gunners.  A 
common  point  for  the  four  pieces  may  be  designated  or  each 
gunner  may  use  a different  point.  In  the  figure  the  gunner  at 
Gi  cannot  see  P2  or  P3,  neither  can  the  gunner  at  G2  see  Pi  or 
P3.  The  gunners  of  the  third  and  fourth  pieces  cannot  see  Pi 
and  P2,  but  they  can  both  see  P3  and  therefore  use  it  in 


190 


GUNNERY 


common.  All  the  gunners  set  their  sights  on  their  new  aim- 
ing point,  pieces  having  already  been  directed. 

Each  gunner  should  chalk  up  the  reading  of  his  sight,  when 
first  directed  upon  the  new  aiming  point,  on  his  gun  shield. 
It  is  apparent  in  Figure  17  that  the  deflection  reading  of  each 
piece  will  be  different  although  the  line  of  fire  of  the  four  gims 
is  parallel.  If  the  batter}^  commander 
attempted  to  shift  the  sheaf  by  designat- 
ing a common  deflection  for  the  guns, 
parallelism  of  fire  would  be  lost,  since 
the  aiming  points  are  not  common. 
Therefore,  the  sheaf  must  be  shifted  to 
the  right  and  to  the  left,  by  subtracting 
and  adding  a common  angle  to  the  indi- 
vidual deflections  of  the  pieces.  It  is 
obvious  that,  if  the  lines  of  fire  are 
parallel  and  each  gunner  add  or  subtract 
100  mils  to  or  from  the  deflections  of  his 
piece,  parallelism  of  fire  will  still  obtain. 

Example  3.  — Combination  of 
Methods. — An  aiming  point  is  visible 
from  the  observing  station  and  from  a 
single  or  several  guns,  but  not  from  all 
the  guns.  (Figure  17.) 

Solution. — The  aiming  point  should 
\ be  employed  by  as  many  guns  as  possi- 
; ble,  the  deflection  for  these  guns  being 
computed  in  the  usual  way.  The  other 
gun  or  guns  may  then  use  the  sight  of  a 
directed  piece  for  an  aiming  point  as  ex- 
plained in  Example  2,  and,  after  being  laid,  employ  a 
secondary  aiming  point.  This  solution  is  merely  a combination 
of  the  regular  method  and  an  expedient.  The  battery  com- 
mander is  constrained,  however,  to  shift  the  sheaf  by  adding 
and  subtracting  instead  of  by  designating  a common  deflection. 


Fig.  18. 


INDIRECT  FIRE  AND  DEFLECTION 


191 


In  Figure  17,  Pi  could  be  employed  to  lay  the  right  piece, 
the  deflection  for  which  having  been  calculated  at  the  station  in 
the  regular  way,  and  the  piece  having  been  laid,  the  gunner 
could  then  assist  the  other  gunners  to  direct  their  pieces  by 
reading  the  deflection  for  the  right  gun  from  the  panoramic 
sights  of  the  other  pieces.  G2,  G3,  G4,  could  then  be  laid  by 
the  use  of  the  panoramic  sight  of  Gi,  as  an  aiming  point,  as 
in  Example  2,  the  direction  of  the  pieces  thereafter  being 
referred  to  the  secondary  aiming  points.  Pi,  P2,  P3. 

Example  4. — C.  Telescope  as  Aiming  Point. — Suitable 
aiming  points  can  be  seen  from  the  guns,  but  none  of  them  are 
visible  from  the  observing  station,  which,  on  account  of  the 
lay  of  the  ground,  must  be  located  on  the  flank  and  at  a con- 
siderable distance  from  the  guns.  The  guns  and  the  station 
are  clearly  visible,  however,  one  from  the  other. 

Solution. — In  Figure  18,  let  T be  the  target,  G the  right 
piece,  and  B the  observing  station.  Let  GB  be  600  yds.,  BT 
2,500  yards  and  GT  2,500  yards. 

A mil  at  T intercepts  2.5  yds.  at  the  guns. 

Therefore 

T = 600  -f-  2.5  = 240  mils. 

Lay  the  B.  C.  telescope  on  G and  measure  the  exterior 
angle  B.  Suppose  it  be  5,000  mils.  Then  the  interior  angle 
h is  known  for 

6 = 6,400  mils  — B 

6 = 6,400  mils  — 5,000  mils. 

- 1,400  mils. 

Now  then  T = 240  mils  and  6 1,400  mils.  Since  the  sum  of 
the  three  angles  of  a triangle  equal  3,200  mils 

d-b6~l“T  = 3,200 
d-3,200-(6-bT) 
d- 3,200 -(1,4004-240) 

= 3,200-1,640 


192 


GUNNERY 


It  is  apparent  then  that  the  angle  d,  that  is  the  angle 
between  the  observing  station  and  the  target,  can  always  be 
computed  at  the  observing  station.  This  being  so,  all  that  is 
necessary  to  direct  the  right  gun  upon  the  target  is  to  lay  the 
piece  with  a deflection  equal  to  this  angle, 
using  the  B.  C.  telescope  as  an  aiming  point. 

The  Drill  Begulations,  1908,  paragraph 
446,  Example  2,  prescribe  a ready  rule, 
which  simplifies  the  calculation.  By  setting 
the  telescope  at  3,200,  directing  it  upon  G 
and  then  upon  T,  the  angle  h is  at  once 
given,  rendering  unnecessary  the  calculation 
of  the  exterior  angle  B and  its  subtraction 
from  6,400  in  order  to  determine  h. 

Let  us  follow  the  rule  in  the  Drill  Regu- 
lations. 

If  the  telescope  be  set  at  3,200  and 
sighted  at  G,  and  then  at  T,  a reading  of 
3,200  less  the  angle  h vdll  be  obtained,  since 
the  telescope  is  turned  to  the  right.  The 
reading  will  be  3,200  — 1,400  or  1,800. 
T==500-r-2.5  = 240.  Subtract  T,  as  the  sta- 
tion is  on  the  right. 

Tig.  19. 

1800—240-1,560 

This  is  the  same  result  before  obtained. 

Now  let  us  compute  the  deflection  when  the  observing 
station  is  on  the  left  (Figure  IQL 

T = — = 250.  ■ 

2 

Read  the  angle  h with  the  telescope.  Suppose  it  be  1,400 
mUs.  Then  d-f-6-fT  = 3,200. 

d = 3,200-6-T  = 3,200  - (6  -j-  T) 

= 3,200- (1,400+250) 

= 1,550. 


INDIRECT  FIRE  AND  DEFLECTION 


193 


This  is  the  value  of  d,  and  not  of  the  exterior  angle  G 
which  the  sights  lay  off.  But  the  angle  G = 6,400 — d 

= 6,400-1,550 
= 4,850 

The  battery  commander  would  then  command: 

1.  Aiming  point  the  B.  C.  telescope. 

2.  By  battery  from  the  right. 

3.  Deflection  4,850. 

4.  Etc.,  etc. 

Following  the  rule  in  the  Drill  Regulations  we  secure  a 
similar  result,  as  follows: 

If  the  telescope  be  set  at  3,200  upon  G and  then  sighted  at 
T a reading  of  3,200+6  or  3,200+1,400  or  4,600  would  be 
obtained. 

BG  is  500  yds.  T = — = 250. 

2 

The  station  is  on  the  left  and  the  value  of  T must  be  added ; 
thus: 

4,600+250  = 4,850. 

The  pieces  having  been  directed  upon  the  target  by  the 
use  of  the  B.  C.  telescope  as  an  aiming  point,  the  direction  of 
the  pieces  may  be  from  now  on  referred  to  the  secondary  aim- 
ing points  visible  from  the  guns.  Should  the  battery  com- 
mander be  forced  to  move  his  station  for  any  reason,  a marker 
should  be  substituted  for  the  telescope,  unless  the  secondary 
aiming  points  are  to  be  used;  otherwise  the  true  direction  would 
be  lost  since  there  would  be  no  common  point  of  reference  for 
the  panoramic  sights  of  the  guns  and  the  combined  effect  of 
uneven  ground,  creeping,  and  jump  would  soon  destroy  the 
effectiveness  of  the  sheaf. 

The  Plotter. — The  plotter  is  a mechanical  device  which 
permits  us  to  transform  the  range  and  direction  of  the  target 


194 


GUNNERY 


as  obtained  at  the  observing  station  so  as  to  make  the  data 
available  for  use  at  the  guns.  By  the  employment  of  this 
instrument  a graphic  solution  is  obtained,  rendering  unneces- 
sary the  use  of  the  formulae. 

At  the  observing  station  the  distances  to  target,  aiming 
point,  and  right  piece  are  measured  by  the  range  finder  or  the 
distances  may  be  estimated.  The  angles 
from  aiming  point  to  target  and  from 
aiming  point  to  right  piece  are  measured 
by  the  B.  C.  telescope.  The  data  as 
found  at  the  observing  station  is  then 
set  off  on  the  instrmnent,  the  protractor 
is  moved  along  its  slide  a distance  corre- 
sponding to  the  distance  between  ob- 
serving station  and  right  piece,  and  the 
range  and  direction  of  the  target  from 
right  piece  are  read  off. 

The  plotter  is  an  exceedingly  valu- 
able instrument  and  vdll,  at  times,  be 
found  all  but  indispensable.  One  diffi- 
culty arises  in  its  use,  however:  fre- 
quently in  a close  country  an  aiming 
point  visible  from  the  guns  cannot  be 
found  sufficiently  distant  from  the  ob- 
serving station  to  permit  of  the  accurate 
calculation  of  deflection  with  the  plotter. 
This  is  the  case  when  an  aiming  point 
on  a flank  of  the  guns  must  be  employed 
which  is  not  1,100  yards  distant  from 
the  station.  In  the  construction  of  the 
plotter,  an  aiming  point  nearer  than 
1,100  yards  to  the  station  was  not  contemplated  and  the  instru- 
ment cannot,  therefore,  be  properly  adjusted  under  such 
circumstances. 

Every  artillery  officer  should  be  as  familiar  vfith  the  use 


Fig.  20. 


INDIRECT  FIRE  AND  DEFLECTION 


195 


of  the  plotter  as  with  that  of  the  B.  C.  telescope.  The  prin- 
ciple of  the  instrument  is  as  follows: — 

Explanation  of  the  Plotter. — Let  us  consider  Figure  20, 
in  which  the  aiming  point,  the  right  gun,  and  the  target  make 
with  each  other  a straight  angle  or  an  angle  of  3,200  mils; 
the  observing  station  being  800  yards  distant  on  the  right 
flank;  the  distances  from  the  station  to  the  target  and  to  the 
aiming  point  being  2,800  and  2,000  yards  respectively. 

The  sum  of  the  three  angles  of  the  lower  triangle,  that  is 
of  the  triangle  GPB,  is  equal  to  3,200  mils.  G = 1,600  mils. 
If  BP  is  2,000  yds.  the  parallax  of  P is  400. 

B+P+G  = 3,200 

B = 3,200 -(P-t-G) 

= 3,200- (400 -H  1,600) 

= 1,200 

In  the  upper  triangle,  or  the  triangle  BTG,  the  sum  of  the 
three  angles  is  also  equal  to  3,200  mils.  G = 1,600.  If  BT  is 
2,800  yds.  the  parallax  of  T is  285. 

B-t-T+G  = 3,200 

B = 3,200 -(T-l-G) 

= 3,200- (285+1,600) 

= 1,315 

The  azimuth  of  T with  respect  to  P is  the  exterior  angle  at 
B,  which  is  equal  to  6,400  mils  less  the  sum  of  the  two  interior 
angles. 

A = 6,400 -(1,315+ 1,200) 

= 6,400-2,515 
= 3,885 

The  azimuth  of  the  right  gun  G with  respect  to  P is  the 
angle  g,  or 

g = 3,885+l,315 
= 5,200 

In  the  right-angle  triangle  BPG  the  square  of  the  hypote- 


196 


GUNNERY 


nuse  is  equal  to  the  sum  of  the  squares  of  the  other  two  sides, 
or 

BP2  = gP^+GB2 
GP2  = BP2-GB2 
GP2  = (2,000)2- (800)2 

= 4,000,000-  640,000  = 3,360,000 ; 

GP  = "^3,360,000=1,835  approximately. 

The  distance  from  right  gun  to  aiming  point  is  therefore 
approximately  1,835  yards. 

In  the  right-angle  triangle  BTG, 

GT2  = BT2-GB2 

= (2,800)2- (800)  2 = 7,200,000 ; 

GT=  "'^7,200,000  = 2,700  approximately. 

The  distance  from  right  gun  to  target  or  the  range  is,  there- 
fore, approximately  2,700  yards. 

Of  course,  the  foregoing  mathematical  calculations  for 
the  azimuths  and  the  distances  are  not  necessary  in  the  field. 
The  angles  are  obtained  in  practice  by  merely  sighting  the 
B.  C.  telescope  first  at  the  auning  point  and  then  at  the  object, 
the  azimuth  of  which  is  desired,  the  distances  being  estimated, 
or  determined  with  the  range  finder.  The  foregoing  solution, 
however,  is  exactly  the  one  given  by  the  plotter.  The  plot- 
ter is  adjusted  as  follows: 

1.  Unclamp  the  arms  of  the  plotter  and  the  arm  slides. 

2.  Clamp  the  protractor  on  the  gun  arm  at  zero. 

3.  Read  the  azimuth  of  the  right  gun  with  respect  to  the 
aiming  point  with  the  B.  C.  telescope. 

4.  Revolve  the  auning  point  arm  until  the  zero  of  the  inner 
circular  scale  is  opposite  the  figure  on  the  outer  circular  scale 
corresponding  to  the  azimuth  of  the  gun;  g in  the  figure  being 
5,200  mil.  Clamp  the  arm. 

5.  Set  the  zero  on  the  slide  of  the  aiming-point  arm  at  the 
point  of  its  scale  corresponding  to  the  distance  of  the  aiming 


INDIRECT  FIRE  AND  DEFLECTION 


197 


point  from  the  observing  station;  2,000  yards  in  the  figure. 
Clamp  the  shde. 

6.  Read  the  azimuth  of  the  target  with  the  B.  C.  telescope. 

7.  Revolve  the  target  arm  of  the  plotter  until  the  zero  of 
its  vernier  scale  is  opposite  the  figure  on  the  outer  circular 
scale  corresponding  to  the  azimuth  of  the  target;  a being  3,885 
in  the  figure.  Clamp  the  arm. 

8.  Set  the  zero  on  the  slide  of  the  target  arm  at  the  point 
of  its  scale  corresponding  to  the  distance  of  the  target  from  the 
observing  station;  2,800  yards  in  the  figure.  Clamp  the  slide. 

9.  Unclamp  the  protractor. 

10.  Turn  the  screw  of  the  protractor  until  the  number  on  the 
scale  of  the  gun  arm,  corresponding  to  the  distance  of  the  right 
gun  from  the  observing  station,  is  brought  opposite  the  zero. 

11.  Clamp  the  protractor. 

12.  The  deflection  of  the  right  gun  is  the  reading  opposite 
the  zero  of  the  vernier  on  the  target  arm.  The  plotter  will 
give  3,200  mils,  which  checks  with  the  geometrical  solution  in 
Figure  20. 

13.  The  range  from  right  piece  to  target  is  the  reading  of 
the  slide  scale  on  the  target  arm.  The  plotter  will  give  about 
2,700  yards. 

14.  The  distance  from  right  piece  to  aiming-point  is  the 
reading  of  the  slide  scale  on  the  aiming-point  arm.  The  plot- 
ter will  give  about  1,835  yards,  which  also  checks  with  the  figure. 

If  the  foregoing  steps  are  followed  out,  the  relative  duec- 
tions  of  the  three  arms  of  the  plotter  will  correspond  to  the 
relative  directions  of  the  aiming  point,  target,  gun,  and  observ- 
ing station  in  Figure  20.  If  in  practice  the  gun  arm  be  pointed 
from  the  observing  station  to  the  right  gun,  when  adjusted, 
the  other  two  arms  should  point  in  the  actual  direction  of  the 
aiming  point  and  target  respectively,  the  instrument  itself 
giving  a graphic  solution  by  the  relative  position  of  its  arms. 

If  there  is  the  slightest  difficulty,  either  in  understanding 
the  principle  of  the  plotter,  or  its  manipulation,  each  of  the 


198 


GUNNERY 


foregoing  steps  should  be  gone  over,  time  and  again,  with  Figure 
20  before  the  eyes.  If  this  be  done  the  trouble  will  soon  be 
disposed  of. 

Measurement  of  Angles. — We  have  seen  that  the  azimuth 
of  the  target,  or  the  horizontal  angle  between  the  aiming  point 
and  the  target,  may  be  measured  by  the  B.  C.  telescope  and 
transformed  so  as  to  give  the  deflection  of  the  right  piece 
either  by  the  parallax  method  (mathematically)  or  by  the 
use  of  the  plotter  (graphically). 

There  are  still  other  ways  in  which  the  azimuth  of  the 
target  may  be  measured,  namely,  by  use  of  the  battery  com- 
mander’s ruler  and  by  measurement  with  the  hand.  It  is 
needless  to  say  that  the  B.  C.  telescope  is  the  most  accurate 
means  and  should  be  used  when  possible  under  all  the  cir- 
cumstances. 

The  B.  C.  Ruler. — The  battery  commander’s  ruler  is  a 
slide  ruler  6.7  inches  long  by  1 inch  wide,  with  a cord  about 
24  inches  long  passing  through  a hole  in  the  center.  (See 
Handbook  of  the  3-Inch  Field  Artillery  Material,  1908,  p. 
114.)  The  instrument  affords  a scale  for  quickly  measur- 
ing azimuths,  a slide  rule  for  determining  the  height  of  the 
trajectory  in  mils  at  any  point  of  the  range,  and  a table  of 
parallaxes  computed  for  a base  of  20  yards  and  varying  ranges 
and  angles  of  obliquity  of  base  to  range.  The  front  or  shde 
face  of  the  ruler  has  the  azimuth  and  height  of  trajectory 
scales;  the  reverse  face  the  parallax  table.  (See  Figure  24.) 

For  measuring  azimuths,  the  scale  on  either  edge  of  the 
slide  face  of  the  ruler  is  used  in  connection  with  the  cord. 
When  one  end  of  the  cord  is  attached  to  the  top  button  of 
the  coat  or  held  in  any  other  convenient  way,  and  the  ruler 
held  horizontal  and  perpendicular  to  the  taut  cord  at  a dis- 
tance of  20  inches  from  the  eye,  the  scale  on  the  edge  of  the 
ruler  measures  in  mils  the  visual  angle  subtended  by  the  cor- 
responding portion  of  the  ruler.  The  cord  supplied  with  the 
ruler  is  sufficiently  long  to  permit  a loop  to  be  formed  for  slip- 


INDIRECT  FIRE  AND  DEFLECTION 


199 


ping  over  the  button  of  the  coat.  The  cord  can  be  adjusted 
to  the  proper  length  by  measuring,  by  means  of  the  telescope 
or  panoramic  sight,  the  angle  subtended  by  the  distance 
between  two  convenient  objects,  and  then  adjusting  the  length 
of  the  cord  so  that  the  ruler  will  give  the  individual  using  it 
the  same  reading.  The  personal  equation  necessarily  enters 
into  the  adjustment  of  the  cord. 

On  one  edge  the  scale  reads  from  0 to  300  mils  and  on  the 
other  edge  from  6,100  through  6,300  to  0.  The  graduations 
are  made  for  every  2 mils  and  figured  for  every  10  mils.  In 
each  case  the  scale  reads  in  the  same  direction  as  the  azimuth 
scale  on  the  panoramic  sight.  The  0 is  also  marked  with  a 
letter  “T”  for  “target,”  since  in  using  the  ruler  that  point  is 
placed  on  the  target. 

This  scale  is  used  for  quickly  finding  the  azimuth  between 
the  target  and  the  aiming  point,  measuring  the  front  of  a 
position,  determining  the  correction  in  azimuth  which  should 
be  made  to  bring  on  to  the  target  projectiles  striking  to  one 
side,  and  similar  data.  It  will  be  especially  useful  when  the 
battery  commander’s  telescope  is  not  available  on  account  of 
lack  of  time  or  for  other  reasons. 

To  use  the  ruler  in  measuring  azimuths,  the  0 (or  “T”)  of 
the  scale  should  be  held  on  the  line  joining  the  eye  and  the 
target  or  other  origin  of  measurements.  If  the  point  the  azi- 
muth of  which  is  required  lies  to  the  right  of  this  origin,  the 
ruler  is  held  in  the  right  hand  and  the  scale  on  its  upper  edge 
is  used.  If,  however,  the  point  the  azimuth  of  which  is  to  be 
determined  lies  to  the  left  of  the  origin,  the  ruler  is  held  in 
the  left  hand  and  the  scale  on  the  lower  edge  is  used,  the  ruler 
being  reversed  to  bring  the  scale  on  top.  The  reading  of  the 
scale  at  the  line  joining  the  eye  and  the  point  then  gives  the 
azimuth  of  this  point  with  reference  to  the  origin.  In  prac- 
tice, the  thumb  and  forefinger  of  the  hand  holding  the  ruler 
are  used  to  mark  the  intersection  of  this  line  and  the  scale. 
(For  use  of  slide  scale  see  subsequent  chapter  on  The  Mask.) 


200 


GUNNERY 


Measurement  by  Hand— If  the  hand  be  held  in  a vertical 
position  at  full  arm-length  from  the  body,  it  will  obliterate 
a portion  of  the  horizon  or  of  the  landscape,  the  amount  obht- 
erated  or  covered  depending  upon  the  length  of  the  arm  and 
the  width  of  the  hand  at  the  point  considered.  The  personal 
equation  enters  largely  into  measurement  by  this  means,  for 
not  only  the  foregoing  factors  but  the  manner  in  which  the 
observer  stands  affects  the  measurement.  Each  observer,  then, 
must  establish  and  observe  a uniform  method  in  order  to 
obtain  even  approximately  uniform  and  accurate  results.  The 
best  method  is  perhaps  that  of  standing  with  the  right  arm 
in  prolongation  of  the  line  of  the  shoulders  and  turning  on  the 
heels  as  the  arm  is  moved  without  changing  the  position  of 
the  heels.  In  this  case  the  position  of  the  heels  is  the  center 
of  a circle,  the  line  from  the  wrist  to  the  center  of  the  body  is 
the  radius,  and  the  arc  of  the  circumference  intercepted  by  the 
width  of  the  hand  is  constant  no  matter  in  what  direction  the 
observer  faces.  The  same  horizontal  line  through  the  hand 
should,  of  course,  always  be  considered. 

Having  adopted  a uniform  method,  it  is  now  necessarj^  to 
determine  the  amount  of  the  circumference  or  the  arc  which 
the  hand  intercepts.  This  may  be  done  as  follows:  Stand- 

ing in  the  position  adopted,  let  the  right  edge  (if  the  right  arm 
is  used)  of  the  hand  rest  upon  a prominent  point  well  removed. 
Note  carefully  the  exact  point  which  clears  the  left  side  of 
the  hand.  Measure  the  angle  between  the  two  points  with 
the  B.  C.  telescope.  Repeat  the  measurement  a number  of 
times,  using  different  objects  in  each  case.  The  sum  of  the 
angles  measured  divided  by  the  number  of  these  angles  will 
give  the  mean  or  average  arc  intercepted  and  the  correspond- 
ing angle  subtended. 

Having  determined  the  mean  value  in  mils  of  the  width  of 
the  hand  held  vertically,  palm  outward,  and  arm  fully  extended, 
an  angle  or  an  arc  may  now  be  measured  by  mo\dng  the  hand 
over  the  arc  to  be  measured  and  multiplying  the  number  of 


INDIRECT  FIRE  AND  DEFLECTION 


201 


successive  movements  necessary  to  cover  the  whole  by  the 
fixed  value  in  mils  of  the  hand. 

With  practice,  measurements  sufficiently  accurate  in  the 
ordinary  case  may  be  obtained  in  this  way. 

Obliquity. — The  parallax  of  a point  the  direction  of  which 
is  normal  to  the 
front  of  the  bat- 
tery, usually  true 
of  the  target,  is 
easily  obtained, 
as  we  have  seen, 
by  dividing  20 
by  the  number 
of  thousands  of 
yards  in  the 
range  of  the 
point;  thus  the 
parallax  of  such 
a point  4,000 
yards  distant  is 
20  divided  by  4, 
or  5 mils. 

The  term 
parallax  is  here 
used  in  a restric- 
ted sense  and  by 
the  parallax  of  a 

point  is  meant 
, , . Fig.  21. 

the  angle  m mils 

subtended  at  the  distance  of  the  point  by  one  platoon  front, 
or  20  yds. 

If  the  direction  of  the  point  is  not  normal  to  the  front  of 
the  battery,  its  parallax  is  not  that  of  a point  equidistant  and 
in  a direction  normal  to  the  line  of  guns. 

In  Figure  21,  let  A be  the  aiming  point  in  a direction  NA, 


202 


GUNNERY 


normal  to  the  line  of  guns  GG.  If  GG  be  a platoon  front  the 
parallax  of  the  aiming  point  is  the  angle  P. 

Now  suppose  the  line  of  guns  in  the  obhque  position  GGi, 
GGi  being  equal  to  GG.  Necessarily  the  aiming  point  is  in 
a direction  N'A  oblique  to  the  line  of  gims.  The  parallax 
of  the  aiming  point  with  respect  to  GG  is  the  angle  P,  but  with 

respect  to  GGi  it  is 
the  angle  P'.  But 
P'  — P-d,  the  angle  d 
measuring  the  de- 
crease in  the  parallax 
due  to  the  obhquity 
of  GGi. 

NA  is  the  normal 
toGG.  N'N'isthe 
normal  to  GGi.  The 
angle  O'  included 
between  the  normals 
measures  the  obliq- 
uity of  A with  re- 
spect to  GGi.  But 
angle  O'  is  equal  to 
the  angle  0 since  the  sides  of  the  two  angles  are  perpen- 
dicular, one  to  the  other. 

It  is  apparent  that  as  the  angle  O,  or  the  obliquity,  increases 
the  greater  is  the  angle  d,  or  the  difference  between  the  normal 
parallax  and  the  actual  parallax. 

The  necessity  for  a correction  for  obliquity  is  also  obvious 
from  Figure  22,  in  which  P'  is  in  a direction  oblique  to  the  line 
of  guns.  The  angle  P'  is  apparently  less  than  the  normal 
angle  P,  the  angle  0 being  the  angle  of  obliquity. 

From  P a platoon  front  appears  to  be  GG,  but  from  P' 
the  platoon  front  is  intercepted  by  the  visual  angle  P'  which  is 
the  normal  parallax  of  GG'  and  not  of  GG.  It  should  be  here 
noted  that  the  amount  of  correction  for  obliquity  increase^ 


INDIRECT  FIRE  AND  DEFLECTION 


203 


with  the  angle  of 
obliquity,  for  the 
larger  the  latter  the 
smaller  the  arc  in- 
tercepted by  the 
visual  angle,  or  the 
smaller  the  actual 
parallax. 

The  value  of  P', 
or  the  actual  paral- 
lax, may  be  deter- 
mined by  trigono- 
metric solution  as 
follows  h 

In  Figure  23  let 

P be  the  normal  parallax  and  P'  the  actual  parallax. 
In  the  right  triangle  P6a; 

ah 


Fig.  23. 


Tangent  | p= — 
ap 


ap  = 

In  the  right  triangle  p'ad, 


ah 


tan  i P 


Tangent  | p'  = —, 
ap 


ap 


ad 


tan  I p' 


^ In  trigonometry  the  sine  of  an  angle  is  the  ratio  of  the  hypotenuse  to  the 

ah 

opposite  side.  Thus  in  Figure  23,  sine  of  O {dab)  is  — . The  cosine  of  an 

ab 

angle  is  its  complementary  sine,  or  the  sine  of  its  complements;  thus  the  cosine 
of  O is  the  sine  of  dab.  The  cosine  of  an  angle  is  the  ratio  of  the  adjacent  side 

to  the  hypotenuse  or  the  cosine  of  O is  — . The  tangent  of  an  angle  is  the 

ab 

. , . . , ab 

ratio  of  the  opposite  to  the  adjacent  side,  or  tangent  of  P is  — . 


204 


GUNNERY 


In  practice  the  distance  ad  is  so  small  in  comparison  with 
dP'  and  aP'  that  the  angle  F'da  may  be  considered  for  aU 
practical  purposes  as  a right  angle.  Hence  the  angle  ahd  is 
taken  as  a right  angle. 

This  being  so,  the  angles 

P'aP  = 90°-Pad 
Vad  — 90° —dab 
P'aP  - dab 
But  P'oP  = 0 
dab  = 0. 

Cosine  ofO  = — ad^ab  cosine  0. 
ab 

ab  ad  ad  ab  cosine  0 

= or  = 

tangent  i P tangent  ^ P'  tan  | P tan  J P' 

tan  I P'  = tan  | P cosine  O 
I P'=  I P cos  0 
P'  = P cos  0. 

Correction  for  Obliquity. — Since,  therefore,  it  has  been 
shown  that  the  actual  parallax  is  equal  to  the  normal  parallax 
multiplied  by  the  cosine  of  the  angle  of  obhquity,  it  becomes 
necessary  in  practice  to  correct  the  normal  parallax  when  the 
point  is  in  a direction  oblique  to  the  line  of  guns. 

In  indirect  firing,  the  aiming  point  is  usually,  and  the  target 
frequently,  located  in  directions  oblique  to  the  front  of  the 
battery  and  in  determining  azimuth  difference  for  adjacent 
guns  in  the  battery  the  parallax  of  both  the  aiming  point  and 
the  target  are  used.  The  foregoing  remarks  about  the  correc- 
tion for  the  obliquity  of  the  aiming  point  also  apply  to  the 
parallax  of  the  target.  The  parallaxes  of  points  for  various 
ranges  and  angles  of  obliquity  have  therefore  been  computed 
and  are  tabulated  on  the  battery  commander’s  ruler  in  a form 
for  convenient  reference.  This  tabulation  is  as  in  Figure  24. 
The  two  upper  lines  of  figures  in  the  table  give  angles  of 


INDIRECT  FIRE  AND  DEFLECTION 


205 


obliquity  for  each  100  mils  in  the  two  quadrants  in  front  of  the 
battery,  while  the  two  lower  lines  give  similar  angles  for  the 
two  quadrants  in  rear.  The  figures  opposite  1,000,  1,250, 
1,500,  and  1,750  are  the  parallaxes  for  these  ranges  at  the  differ- 
ent angles  of  obliquity  given  in  the  table.  For  higher  ranges 
simple  multiples  of  the  tabular  ranges  are  taken.  Thus,  for 
3,500  yards  take  one-half  of  the  parallax  for  1,750  yards; 
for  5,000  yards  take  one-fifth  of  the  parallax  for  1,000  yards, 
or  one-fourth  of  that  for  1,250  yards,  etc. 

In  using  the  table,  interpolation  is,  as  a rule,  unnecessary. 
It  is  sufficiently  accurate  for  all  practical  purposes  to  take  the 
direction  of  the  point  to  the  nearest  100  mils  and  the  range  to 


1 PARALLAX  1 

FRONT 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

0 

63 

62 

61 

60 

59 

58 

57 

56 

55 

54 

53 

52 

51 

50 

49 

48 

HDS.MILS. 

YARDS 

1000 

20 

20 

20 

19 

18 

18 

17 

15 

14 

13 

11 

9 

8 

6 

4 

2 

0 

1250 

16 

16 

16 

15 

15 

14 

13 

12 

11 

10 

9 

8 

6 

4 

3 

2 

0 

1500 

13 

13 

13 

13 

12 

12 

11 

10 

9 

8 

7 

6 

5 

4 

3 

1 

0 

1750 

11 

11 

11 

11 

11 

10 

9 

9 

8 

7 

6 

5 

4 

3 

2 

1 

0 

REAR 

32 

31 

30 

29 

28 

27 

26 

25 

24 

23. 

22 

21 

20 

19 

18 

17 

16 

32 

33 

34 

35 

36 

37 

38 

39 

40 

41 

42 

43 

44 

45 

46 

47 

48 

Fig.  24. 


the  nearest  tabular  one  or  to  the  nearest  multiple.  Thus,  for 
a point  whose  range  is  2,800  yards,  and  whose  direction,  as 
given  by  the  B.  C.  telescope,  is  3,360,  enter  the  table  with  a 
range  of  3,000  yards  (2X1,500)  and  take  out  the  parallax  cor- 
responding to  34  (3,400),  which  in  this  case  is  found  to  be  one- 
half  of  13,  or  6.5.  As  the  actual  range  is  2,800  yards  and  the 
angle  3,360,  both  less  than  the  tabular,  7 should  in  this  case 
be  taken  as  the  parallax  required. 

In  using  the  table,  note  that  the  angle  of  obliquity  of  the 
point  whose  parallax  is  desired  is  measured  from  the  normal 
to  the  front  of  the  battery  and  is  the  azimuth  of  the  point 


206 


GUNNERY 


with  reference  to  that  normal.  The  target  is  always  in  the 
first  or  fourth  quadrant  and  is  usually,  but  not  always,  so 
nearly  normal  to  the  front  of  the  battery  that  its  angle  of 
obliquity  may  be  neglected.  The  aiming  point  may,  however, 
be  located  in  any  direction  and  its  angle  of  obliquity  may, 
therefore,  vary  from  0 to  6,400. 

The  values  of  the  parallaxes  obtained  from  the  table  are 
used  by  the  battery  commander  in  determining  sight  deflec- 
tion, etc.,  in  accordance  with  the  methods  hereinbefore  ex- 
plained. In  correcting  the  parallax  of  the  aiming  point  for 
obliquity  it  is  usually  sufficiently  accurate  to  consider  the 
deflection  of  the  right  piece  as  indicating  the  degree  of  obliquity 
of  the  aiming  point. 

Ready  Rule  for  Correcting  for  Obliquity. — The  angle  of 
obliquity,  as  we  have  seen,  is  the  angle  between  the  normal 
to  the  line  of  guns  and  the  line  of  direction  of  the  aiming  point. 
The  angle  which  the  latter  line  makes  with  the  line  of  guns  is 
necessarily,  therefore,  the  complement  of  the  angle  of  obliq- 
uity, and  the  cosine  of  the  former  is  the  sine  of  the  latter 
angle. 

From  the  foregoing  we  deduce  the  ready  rule  that:  the 
normal  'parallax  multiplied  hy  the  natural  sine  of  the  angle 
between  the  line  of  guns  and  line  of  direction  of  aiming  point  or 
target  gives  the  actual  parallax;  or: 

P'  = P X sine  angle  of  direction  with  line  of  guns. 

The  natural  sines  of  the  angles  22|°,  45°  and  67|°  are 
approximately  4,  7,  and  9,  respectively.  But  these  angles 
correspond  to  angles  of  400  mils,  800  mils  and  1,200  mils 
respectively. 

To  illustrate  the  application  of  the  ready  rule,  let  us  take 
an  aiming  point  directly  in  rear  and  azimuths  for  three  tar- 
gets of  2,000  mils,  2,400  mils,  and  2,800  mils,  respectively. 
Suppose  T in  each  case  is  10. 

A line  to  the  first  target  makes  an  angle  of  400  mils  with 
the  line  of  guns.  T'i  = Ti  X sine  of  400  mils  = 10  X .4  = 4. 


INDIRECT  FIRE  AND  DEFLECTION 


207 


A line  to  the  second  target  makes  an  angle  of  800  mils  with 
the  line  of  guns  and  T'2  = T2  X sine  of  800  mils  =10  X .7  = 7. 

A line  to  the  third  target  makes  an  angle  of  1,200  mils  with 
the  line  of  guns  and  T's  = T3  X sine  of  1,200  mils  = 10  X .9  = 9. 

Thus,  we  see  that  as  the  angle  of  direction  approaches  the 
normal  the  difference  between  the  normal  and  the  actual  paral- 
lax grows  less. 

But  suppose  the  azimuth  be  2,200  mils.  For  2,000  mils  the 
natural  sine  of  the  angle  of  direction  with  the  line  of  guns  is 
that  of  an  angle  of  400  mils  or  .4,  and  for  an  azimuth  of 
2,400  mils  with  aiming  point  in  rear  the  natural  sine  of  the 
angle  of  direction  with  the  line  of  guns  is  .7.  Therefore,  the 
natural  sine  of  the  angle  of  direction  for  an  azimuth  of  2,200 
mils,  or  an  angle  half-way  between  2,000  mils  and  2,400  mils, 
is  approximately  half-way  between  .4  and  .7  or  .55. 

The  only  figures  that  it  is  necessary  for  an  officer  to  remem- 
ber in  correcting  for  the  obliquity  of  the  aiming  point  and  the 
target  are: 

Angle  of  Direction  with  Line  of  Guns.  Multiply  Normal  Parallax  by 


400  mils 

.4 

800  mils 

.7 

1,200  mils 

.9 

Problem. — The  line  of  guns  runs  east  to  west;  the  aiming 
point  is  due  southwest  and  the  azimuth  is  3,400;  P is  — 10  and 
T is  4.  Correct  for  obliquity. 

Solution. — The  direction  of  the  aiming  point  is  at  an  angle 
of  45°  or  800  mils,  in  the  lower  left  quadrant,  with  line  of 
guns.  For  800  mils  the  proper  correction  figure  is  .7,  and 

P'  = P X .7=— 10X.7  = — 7 or 
Corrected  parallax  of  aiming  point  = — 7. 

The  direction  of  the  target  is  at  an  angle  of  1,000  mils  in 
the  upper  right  quadrant  with  the  line  of  guns.  For  800  mils 
the  correction  figure  is  .7  and  for  2,200  mils  it  is  .9;  1,000  mils 


208 


GUNNERY 


is  midway  between  800  mils  and  200  mils.  Therefore  the 
correction  figure  is  taken  as  .8: 

T'  = TX.8  = 4X.8  = 3.2  or 
Corrected  parallax  of  target  = 3 
P—7  T = 3 
D-A+n  (P— T) 

= 3,400  + 10(— 7— 3)  =3,400 +10(— 10)  =3,400— 100  = 3,300. 

Whereas,  if  there  had  been  no  correction  for  obliquity  the 
following  result  would  have  been  obtained: 

D = A+n  (P— T) 

= 3,400+10  (—10—4)  = 3,400+10  (—14)  = 3,400  - 140  = 3,260. 

Thus  an  error  in  deflection  of  40  mils  would  have  been 
made  and,  since  the  range  is  7,000  yds.  when  T = 3,  the  pro- 
jectiles would  have  carried  280  yards  to  the  right  of  the  target. 


CHAPTER  III 


RANGE  AND  RANGING 

The  range  is  the  distance  of  the  target  from  the  guns.  This 
range  must  be  distinguished  from  the  ballistic  range.  The 
latter  may  be  shorter  or  greater  than  the  former.  The  bal- 
listic range  depends  upon  the  elevation  of  the  gun  and  the 
consequent  trajectory  while  the  range  of  the  target  is  not 
affected  by  the  adjustment  of  the  piece. 

Ranges  for  light  artillery  are  classified  in  the  Field  Service 
Regulations,  1910  (Sec.  255,  p.  159),  as  follows: — 

Distant,  Over  4,500  yards. 

Long,  4,500  to  3,500  yards. 

Effective,  3,500  to  2,500  yards. 

Close,  Under  2,500  yards. 

A “point  blank”  range  is  one  which  requires  no  elevation 
on  the  part  of  the  gun,  or  it  is  the  distance  a projectile  will 
travel  in  a straight  line  regardless  of  the  tendency  of  gravity 
to  pull  it  toward  the  earth. 

The  extreme  range  of  a piece  is  the  maximum  distance  the 
gun  is  capable  of  throwing  a projectile.  Distant  ranges  are 
often  erroneously  spoken  of  as  extreme  ranges. 

The  maximum  effective  range  of  a 3-inch  gun  is  3,500 
yards.  The  maximum  range  at  which  the  piece  is  effective 
is  from  7,000  to  7,500.  This  distinction  should  be  borne  in 
mind. 

Range  may  be  determined  by  means  of  range-finding  instru- 
ments, by  the  B.  C.  telescope  and  a measured  base  (Trigono- 
metric and  Geometric  Calculations),  by  the  use  of  scaled 

209 


210 


GUNNERY 


maps,  by  sound,  and  by  estimation.  Upon  the  accurate  deter- 
mination of  range  all  other  calculations  depend,  even  those  for 
direction  when  the  parallax  method  is  employed.  The  dis- 
tance to  the  aiming  point  may  be  determined  in  the  same  man- 
ner as  the  range. 

The  velocity  of  sound  at  a temperature  of  50°  F.  is  about 
1,110  feet  per  second.  The  velocity  increases  about  a foot  per 
second  for  each  degree  of  temperature.  The  velocity  is  also 
affected  by  the  wind,  but  if  we  multiply  the  number  of  seconds 
from  the  time  the  puff  of  smoke  from  a shrapnel  is  seen  to 
the  time  the  explosion  is  heard  by  the  figure  1,100  the  result 
will  be  the  range  in  feet. 

The  formula  for  the  calculation  of  velocity  of  sound  through 
air,  when  t = temperature  in  degrees  Centigrade,  is: 

V = 1,090  Vl  + . 00366 1. 

By  constant  practice  it  is  possible  to  gain  the  ability  to 
estimate  distances  very  closely,  and  it  is  imperative  that  an 
artilleryman  should  acquire  this  ability.  ^^Tien  the  range  is 
estimated,  the  estimation  is  verified  by  trial  shots  before  fire 
for  effect  is  commenced. 

The  adjustment  in  range  involves  the  determination  of  a 
range  setting  which  will  cause  the  mean  trajectory  to  pass 
through  the  target,  or,  if  this  is  not  practicable,  the  range 
settings  corresponding  to  the  front  and  rear  limits  of  a zone 
which  surely  contains  the  target. 

The  adjustment  of  the  range  is  preferably  based  upon  the 
observation  of  percussion  bursts.  If  the  ground  in  rear  or  in 
front  of  the  target  or  registration  mark  can  be  seen,  the  tar- 
get must  be  bracketed  between  such  bursts.  If  the  ground 
cannot  be  seen,  then  the  target  must  be  bracketed  between 
low  bursting  time  shrapnel. 

It  is  rarely  possible  from  a position  near  the  guns  to  esti- 
mate with  any  accuracy  the  amount  of  the  error  in  range.  Such 
estimates  are  usually  too  small  and  timid,  and  insufficient 


RANGE  AND  RANGING 


211 


changes  in  the  range  are  consequently  made.  Delay  in  adjust- 
ing the  fire  thus  often  results. 

Attention  should  rather  be  concentrated  on  deciding 
whether  salvos  or  shots  are  short  or  over,  and  on  quickly 
inclosing  the  target  with  fire  which  is  surely  short  and  fire 
which  is  surely  over. 

By  gradually  narrowing  the  bracket  thus  determined  an 
accurate  adjustment  may  be  secured. 

A salvo  is  termed  short  ( — ) if  the  majority  of  its  bursts  are 
short,  over  (+)  if  the  majority  are  over,  and  bracketing  (-h) 
if  half  are  short  and  half  are  over.  Bursts  at  the  target  may 
be  included  either  with  the  shorts  or  the  overs,  as  the  circum- 
stances dictate. 

If  the  bursts  of  a bracketing  salvo  occur  on  graze,  the  indi- 
cation is  that  the  range  of  the  salvo  was  correct;  if  they  occur 
in  air,  that  the  range  was  approximately  correct,  but  somewhat 
too  great. 

If  the  sense  of  a salvo  cannot  be  definitely  decided  upon,  it 
should  be  noted  as  doubtful  (?)  and  disregarded. 

The  observer  should  train  himself  to  decide  quickly  upon 
the  sense  of  a salvo  as  short,  over,  bracketing,  or  doubtful. 
It  may  be  necessary,  however,  to  allow  time  for  the  smoke  to 
form  and  reveal  its  relative  position  with  respect  to  the  target. 

If  the  observer  is  at  a considerable  elevation  above  the 
target,  or  the  target  is  on  ground  sloping  toward  the  observer, 
the  sense  of  a salvo  (short  or  over)  may  usually  be  recognized 
readily  by  noting  the  relative  position  with  respect  to  the  tar- 
get of  burst  on  graze  or  fragmental  hits  from  bursts  in  air. 

But  if  the  target  and  its  vicinity  cannot  be  seen  from  a 
superior  elevation,  if  the  ground  near  the  target  is  at  about  the 
same  elevation  as  the  observer,  or  if  the  ground  in  front  or 
rear  of  the  target  cannot  be  viewed,  the  deductions  as  to  the 
sense  of  the  salvo  are  to  be  formed  especially  from  the  manner 
in  which  the  pufis  of  smoke  from  the  bursts  appear  with  respect 
to  the  targets. 


212 


GUNNERY 


A burst  on  graze  causes  a column  of  smoke  and  dirt  to  be 
thrown  up  from  the  ground,  In  the  case  of  a shrapnel  this 
column  is  relatively  small  and  fugitive;  in  the  case  of  a shell 
it  is  large  and  remains  visible  for  some  time, 

A burst  in  air  produces  a ball  of  smoke  which  ordinarily 
remains  together  for  some  time. 

The  bullets  and  fragments  from  a burst  in  air  knock  up  a 
considerable  amount  of  dirt  and  dust  if  they  strike  dry  soil; 
on  wet  soil  splashes  of  mud  are  knocked  up  by  the  shrapnel 
case  and  large  fragments.  In  either  case  valuable  indications 
are  thus  furnished  as  to  where  the  trajectory  prolonged  reaches 
the  ground. 

If  the  target  is  silhouetted  against  the  smoke  of  the  burst, 
the  range  may  always  be  considered  as  over,  whether  the  burst 
occurred  in  air  or  on  graze. 

If  the  target  is  obscured  by  the  smoke  of  the  burst,  the 
range  may  be  considered  as  short;  but  in  the  case  of  a burst 
in  air  the  burst  must  be  low  in  order  to  warrant  this  conclusion. 

If  the  target  is  indistinct  and  of  about  the  same  color  as 
the  smoke,  it  may  be  less  visible  against  the  smoke  as  a back- 
ground than  against  its  natural  background.  A burst  beyond 
the  target  may,  for  this  reason,  sometimes  seem  to  obscure 
the  target  and  hence  be  judged  short,  when  it  is  in  reality  over. 
On  the  other  hand,  some  targets  become  very  much  more 
visible  if  projected  against  a smoke  background. 

If  the  wnnd  is  blowing  up  or  down  the  range,  a decision 
should  be  formed  quickly  as  to  the  relative  position  of  the  smoke 
with  respect  to  the  target.  But  if  the  wind  is  bloving  across 
the  range  it  may  be  better  to  wait  until  the  smoke  has  drifted 
across  the  front  or  rear  of  the  target.  To  secure  this  latter 
result  it  may  be  desirable  to  direct  the  fire  for  adjustment  at 
the  windward  flank  of  the  target. 

It  is  necessary  to  study  carefully  the  ground  near  the  tar- 
get and  locate  ravines  or  hollows  which  might  catch  and  hide 
the  bursts  of  projectiles.  The  smoke  from  such  bursts  is  apt 


RANGE  AND  RANGING 


213 


to  rise  and  reveal  itself  after  a time,  but  false  deductions  may- 
be drawn  from  it.  Thus  the  smoke  from  a burst  short  of  the 
target  may  have  become  so  much  dissipated  by  the  time  it 
appears  that  the  target  may  be  seen  through  it  and  the  impres- 
sion produced  that  the  target  is  silhouetted  against  the  smoke. 
Moreover,  if  a strong  cross-wind  is  blowing,  the  smoke  when  it 
appears  will  probably  be  at  some  distance  to  the  flank  of  the 
actual  point  of  burst,  and  erroneous  conclusions  as  to  the 
direction  of  the  salvo  may  thus  be  reached.  Such  false  deduc- 
tions may  be  avoided,  however,  if  the  lay  of  the  ground  is 
appreciated  and  taken  into  consideration. 

In  adjusting  Are  upon  a crest  great  care  must  be  taken  to 
reach  this  crest  and  not  be  deceived  by  a crest  parallel  to  the 
crest  sought,  but  short  of  it.  In  rolling  country  such  an  inter- 
mediate crest  is  often  present,  and  it  may  merge  itself  into  the 
background  formed  by  the  higher  ground  in  its  rear,  and  hence 
escape  detection,  while,  as  a matter  of  fact,  there  may  be  a 
broad  valley  or  depression  between  the  two  crests.  Shots 
which  strike  on  the  near  side  of  the  intermediate  crest  may  be 
taken  as  estabhshing  the  short  limit  of  the  bracket,  while 
shots  which  pass  over  the  intermediate  crest,  burst  low  or  on 
graze  in  the  valley  between  the  two,  and  are  lost,  may  be  con- 
sidered to  have  cleared  the  fmther  crest,  and  hence  may  be 
taken  as  estabhshing  the  long  limit  of  the  bracket.  Such 
deceptions  may  be  avoided  by  obtaining  bursts  in  air  on  the 
line  joining  observer  and  the  crest  sought.  If  the  ball  of 
smoke  is  cut  in  two  by  the  crest  and  the  crest  clearly  deflned 
against  it,  the  shot  is  over,  while  if  the  crest  is  concealed  by 
the  smoke  the  shot  is  short.  The  short  bursts  may  often 
serve  to  reveal  the  existence  of  the  intermediate  crest  by  caus- 
ing the  latter  to  be  silhouetted  against  the  smoke. 

The  existence  of  unexpected  ra^dnes  and  hollows  may  some- 
times be  deduced  from  the  fact  that,  while  bursts  in  air  are 
seen,  the  points  of  impact  of  the  fragments  with  the  ground  are 
not  revealed  by  the  dust  and  dirt  knocked  up. 


214 


GUNNERY 


If  the  sun  is  shining,  information  as  to  the  sense  of  bursts 
in  air  may  often  be  obtained  by  observing  the  shadow  on  the 
ground  of  the  ball  of  smoke  produced  by  the  bursts.  The 
height  of  the  burst  and  the  position  of  the  sun  must,  however, 
be  taken  into  consideration. 

If  the  sense  of  the  burst  or  bursts  is  doubtful,  circumstances 
must  decide  whether  to  repeat  the  salvo  or  round  or  to  change 
the  firing  data  for  the  next  salvo  or  round. 

If  smoke  or  the  fire  of  other  batteries  has  interfered  with 
observation,  a salvo  concentrated  upon  some  prominent  part 
of  the  target  may  be  of  assistance. 

If  the  doubt  was  occasioned  by  the  fact  that  the  bursts 
were  in  air  and  high,  it  may  be  well  to  merely  diminish  the 
corrector  for  the  next  salvo.  The  sense  of  such  salvos  may 
often  be  determined,  however,  by  observing  the  points 
X3600  Qf  impact  of  the  shrapnel  cases. 

If  a salvo  is  lost,  the  projectiles  have  probably 
X3200  burst  in  a ravine  or  behind  some  intervening  cover.  If 
the  smoke  of  the  bursts  does  not  rise  and  become  visible 

Ty  3000 

after  a few  seconds,  the  lay  of  the  ground  wdll  determine 
X2800  whether  to  increase  or  diminish  the  range  or  to  merely 
increase  the  corrector  so  as  to  obtain  visible  bursts  in 
air.  Definite  information  may  generally  be  most 
quickly  obtained  in  such  cases  by  securing  time  bursts 
just  above  the  level  of  the  crests  or  other  cover. 

The  foregoing  remarks,  taken  from  the  Drill  Regu- 
^ lations,  are  pregnant  with  suggestion  based  on  actual 
Fig  1 experience,  and  should  be  studied  carefully.  'V\Tiile  it 
is  impossible,  on  paper,  to  consider  a case  of  bracketing 
subject  to  the  varied  conditions  of  actual  practice,  it  will  be 
well  to  illustrate  a normal  case. 

Suppose,  in  Fig.  1,  that  T is  the  target  and  G the  gun  and 
that  the  estimated  range  is  3,600  yards.  The  first  shot  or 
salvo  gives  an  over  burst.  The  great  danger  is  that  the  obser- 
ver will  endeavor  to  save  time  by  an  attempt  to  adjust  with 


RANGE  AND  RANGING 


215 


the  next  shot.  Almost  invariably  the  effort  will  result  in  a 
waste  of  both  time  and  ammunition.  When  the  first  shot  is 
over  the  range  should  be  reduced  400  yards.  Suppose  this 
shot  is  over.  The  next  range  would  be  2,800  yards.  If  this 
shot  is  short  the  bracket  has  been  secured.  The  original 
bracket  is  400  yards  and  should  always  be  split,  however 
close  the  short  shot  may  appear,  unless  the  fire  is  adjusted. 
The  next  range  would  be  3,000  yards  and  adjustment  would  be 
complete  provided  a 1-mil  height  of  burst  had  been  secured. 
The  corrector  should  then  be  raised  to  give  a 3-mil  height  of 
burst  and  fire  for  effect  commenced. 

If  in  ranging  by  trial  shots  or  salvos,  the  bursts  are  not 
visible,  it  may  be  that  the  terrain  between  the  observation 
station  and  the  target  is  such  (dense  thickets  or  deep  folds  in 
the  ground  or  the  two  combined)  that  the  sense  of  the  shots 


cannot  be  determined.  All  that  can  then  be  done  is  to  be 
assured  that  the  estimate  of  the  range  is  as  close  as  possible, 
check  up  the  angle  of  sight,  and  raise  the  corrector  until  the 
burst  appears.  With  the  sense  of  a visible  burst  determined 
a bracket  can  then  be  secured  and  adjustment  follows.  The 
corrector  should  be  boldly  raised,  not  less  than  5 points  at  a 
time.  Smaller  alterations  very  generally  result  in  the  waste 
of  too  much  ammunition  even  if  time  is  of  no  importance. 

Let  us  suppose  now  that  we  are  firing  at  T,  in  Figure  2, 
and  that  the  first  shot  is  lost;  corrector  28,  range  4,000  yds. 

If  we  raise  our  corrector  to  33  and  still  get  no  burst,  the 
shot  may  be  over  2 or  short  2.  If  the  next  shot  with  corrector 
38  gives  a burst  at  3 with  the  same  range  it  is  very  probable 
that  we  will  detect  from  the  height  of  burst  above  the  target 


216 


GUNNERY 


that  our  range  is  too  great.  At  any  rate,  we  will  at  once 
bracket  and  get  a short. 

Now  if  the  burst  were  secured  with  corrector  38,  consider- 
ably short  of  the  target  at  3,  on  the  third  shot  we  would  hold 
at  corrector  38  and  increase  the  range  400  yds.  until  we  got  a 
bracket.  If  we  had  raised  the  corrector  a point  or  so  at  a 
time  it  would  have  taken  many  more  rounds  to  adjust. 

In  practice  the  difficulty  of  adjusting  is  increased  by  the 
error  of  the  fuse.  When  the  fuse  is  set  for  a 1-mil  height  of 
burst,  from  I to  i of  the  shrapnel  fired  will  burst  on  graze, 
and  with  a fuse  set  for  a mean  height  of  3 mils  about  l/lO  will 
burst  on  graze.  Trial  sai^os  in  rugged  country  are  therefore 
more  satisfactory  than  single  shots,  for  one  or  more  bursts 
will  almost  always  be  secured  at  the  mean  height  in  spite  of 
the  error  of  the  fuse. 

Under  the  heading  of  Range  the  corrector  will  not  be  treated 
fm-ther,  as  a special  chapter  will  be  given  to  the  subject. 

Depending  upon  the  nature  of  the  target  and  upon  the 
accuracy  with  which  the  adjustment  has  been  secured,  the 
fire  for  effect  may  be  of  two  general  kinds,  viz.:  (1)  Fire  at  a 
single  range,  and  (2)  Fire  at  successive  ranges  (or  searching 
fire). 

Fire  at  a single  range  is  appropriate  when  the  firing  data 
for  the  enemy’s  position  have  been  determined  by  previous 
fire.  Thus  it  is  adapted  to  the  attack  of  all  stationary  tar- 
gets upon  which  an  exact  adjustment  has  been  secured,  or  for 
the  attack  of  moving  targets  as  they  reach  a position  upon 
which  the  fire  has  been  previously  registered.  If  the  fire  is 
properly  adjusted,  the  necessary  effect  may  be  produced  with 
the  minimum  expenditure  of  ammunition. 

Fire  at  successive  ranges  is  appropriate  when  it  has  been 
impracticable  to  secure  exact  adjustment  upon  the  target. 
Due  to  uncertainties  of  observation,  especially  at  long  ranges, 
exact  adjustment  is  often  difficult  of  attainment;  vdthin  the 
time  allowed  by  the  tactical  conditions  it  may  be  impossible 


RANGE  AND  RANGING 


217 


of  attainment.  In  such  cases  the  preferable  course  is  to  inclose 
the  target  within  the  smallest  limits  that  can  be  determined 
with  surety  and  reasonable  promptness,  and  then  to  search 
the  area  thus  inclosed  by  fire  at  successive  ranges. 

If  possible,  a 100-yard  bracket  is  always  obtained,  and  the 
fire  is  dehvered  at  the  short,  the  mid,  and  the  extreme  ranges 
of  this  bracket  until  the  most  effective  range  can  be  deter- 
mined. Whatever  the  limits  determined,  however,  the  fire 
is  closely  observed,  ranges  which  are  evidently  ineffective  are 
rejected,  and  the  area  to  be  searched  thus  gradually  reduced 
to  the  smallest  possible  limits. 

Weldon  Range  Finder. — The  object  of  these  lectures  is 
not  to  improve  upon  the  excellent  service  manuals,  regula- 
tions, etc.,  with  which  the  field  artilleryman  is  supplied,  but 
merely  to  elucidate  the  principles  upon  which  the  prescribed 
methods  are  based,  for  if  the  reason  for  each  step  is  understood 
the  prescribed  methods  are  much  simpler  to  understand. 

Before  the  Weldon  Range  Finder  can  be  intelligently 
employed  the  observer  must  have  some  shght  knowledge  of 
optics.  It  is  true  he  may  learn  to  use  the  instrument  success- 
fully in  a mechanical  way  but  sooner 
or  later  he  will  become  lost,  for  he  is 
necessarily  working  in  the  dark. 

If  a beam  of  the  sun’s  rays  AB  (Fig. 

3)  be  admitted  through  a small  hole  in 
the  shutter  of  a dark  room,  and  allowed 
to  fall  on  a mirror  or  a polished  plane 
surface,  it  will  be  seen  to  continue  its 
course  in  a different  direction  BC.  This 
is  an  example  of  reflection. 

AB  is  called  the  incident  beam,  and  BC  the  reflected  beam. 
The  angle  ABD  contained  between  an  incident  ray  and  the 
normal  is  called  the  angle  of  incidence;  and  the  angle  CBD 
contained  between  the  corresponding  reflected  ray  and  the 
normal  is  called  the  angle  of  reflection.  The  plane  containing 


218 


GUNNERY 


the  incident  ray  and  the  normal  ray  is  called  the  plane  of 
incidence. 

The  reflection  of  light  from  polished  surfaces  takes  place 
according  to  the  following  laws: — 

1.  The  reflected  ray  lies  in  the  plane  of  incidence. 

2.  The  angle  of  reflection  is  equal  to  the  angle  of  incidence. 
These  laws  must  be  constantly  borne  in  mind  in  order  to 

understand  the  phenomena  of  reflection. 

Now  suppose  the  ruled  portion  of  Figure  4 represents  a 
plowed  field,  the  unruled  portion  a smooth  surface,  and  that 
a company  of  infantry  is  marching  in  the  line  aa.  The  two 
flanks  are  on  a line  with  each  other.  It  is  obvious  that  as  the 


line  advances,  hh,  a portion  of  the  men  will  be  marching  in 
the  plowed  field  while  the  left  is  still  advancing  on  the  smooth 
ground.  If  the  left  continues  at  the  same  rate,  the  right  will 
fall  behind  somewhat,  due  to  the  roughness  of  the  ground. 
This  is  exactly  what  happens  to  a ray  of  light  when  it  strikes 
a denser  medium.  The  ray  is  deflected  from  its  original  direc- 
tion. We  have  all  seen  how  the  direction  of  a sunbeam  is 
changed  by  a window-pane.  The  phenomenon  is  known  in 
optics  as  refraction. 

Refraction  then  is  the  deflection  or  bending  which  raj's  of 
light  experience  in  passing  obliquely  from  one  medium  to 
another;  for  instance,  from  air  into  water.  Refraction  due 
to  water  is  illustrated  by  trying  to  strike  a fish  with  a spear. 
The  fish  is  never  quite  where  it  appears  to  be,  unless  one  stands 


RANGE  AND  RANGING 


219 


immediately  above  it.  If  the  incident  ray  is  perpendicular 
to  the  surface  separating  the  two  media,  it  is  not  bent,  but 
continues  in  its  original  course.  And  so  would  the  troops 
keep  in  line  if  they  all  struck  the 
ploughed  field  at  the  same  time. 

The  incident  ray  being  repre- 
sented by  SO  (Fig.  5),  the  re- 
fracted ray  is  the  direction  OH 
which  light  takes  in  the  second 
medium,  and  of  the  angles  SOA 
and  HOB,  which  these  rays  form 
with  the  normal  AB,  to  the  sur- 
face which  separates  the  two 
media;  the  first  is  the  angle  of 
incidence,  and  the  other  the  angle  of  refraction.  According  as 
the  refracted  ray  approaches  or  deviates  from  the  normal,  the 
second  medium  is  said  to  be  more  or  less  refracting  than  the  first. 

The  fluid  envelope  of  the  earth,  or  the  atmosphere,  is  so 

much  denser  than  the  rarefied 
space  beyond  that  the  light  from 
a star  is  refracted  and  the  star  is 
not  actually  where  it  appears  to  be. 

Now  if  a piece  of  transparent 
glass  or  quartz  with  'ground  plane 
faces  be  used  as  a medium,  refrac- 
tion occurs;  the  change  of  direction 
of  the  light  depending  upon  the 
relative  positions  of  the  faces  of 
the  refractory  medium.  Such  a 
medium  is  called  a prism,  the 
word  prisma  meaning  something 
sawed,  from  the  Greek  verb,  pmem, 
to  saw.  Optical  prisms  are  usually  sawed  and  ground  from 
the  material  of  which  they  are  composed. 

The  laws  of  refraction  are  such  that  the  angle  of  refraction 


220 


GUNNERY 


Fig.  7. 


of  a triangular  prism  is  equal  to  the  angle  between  the  faces 
or  the  inclination  of  the  sides. 

Thus,  in  Figure  7,  if  0 be  a luminous  point  or  a visible 
object,  the  ray  is  refracted  at  D and  is  deflected  to  K in  passing 

through  the  denser  medium,  just  as 
was  the  hne  of  troops  by  the  plowed 
field.  At  K the  ray  passes  into  the 
air,  a less  refractive  medium  than 
glass,  and  again  changes  direction. 

The  light  is  thus  refracted  twice 
in  the  same  direction,  first  toward  the 
base  of  the  triangular  prism,  so  that 
to  the  eye  which  receives  the  emergent  ray  KE,  the  image 
appears  to  be  at  O'  instead  of  at  O.  O'  is  called  the  \drtual 
image.  The  word  virtual  is  used  because  it  means,  not  in 
fact,  not  actual,  but  equivalent  so  far  as  effect  is  concerned. 

Objects  seen  through  a triangular  prism  always  appear 
deflected  toward  its  sum- 
mit, A.  The  angle  be- 
tween the  incident  ray 
OEO'  expresses  the  devi- 
ation of  the  light  and  is 
called  the  angle  of  devi- 
ation. This  angle  not 
only  depends  upon  the 
angle  of  refraction  but 
upon  the  angle  at  which 
the  ray  enters  the  prism 
or  the  angle  of  incidence. 

An  isosceles  right- 

angle  prism  clearly  illustrates  the  fact  that  the  angle  of 
deviation  is  equal  to  the  angle  of  refraction  or  the  angle  be- 


•0' 


tween  the  faces.  (Figure  8.) 

Let  ABC  be  the  principal  section  (a  section  perpendicular 
to  its  edge)  of  such  a prism;  O a luminous  object;  and  OH  a 


RANGE  AND  RANGING 


221 


ray  at  right  angles  to  the  face  BC.  This  ray  enters  the  glass 
without  being  refracted,  because  it  is  normal  to  BC.  It 
makes  with  the  face  AB  an  angle  equal  to  B — that  is,  45°. 
(In  an  isosceles  right-angle  triangle  two  of  the  angles  are  45°.) 
The  ray  OH  undergoes,  therefore,  at  H total  reflection,  which 
imparts  to  it  a direction  HI  (since  angle  of  reflection  equals 
angle  of  incidence)  perpendicular  to  the  second  face  AC.  Thus 
the  hypotenuse  surface  (AB)  of  this  prism  produces  the  effect 


of  the  most  perfect  plane  mirror,  and  an  eye  placed  at  I sees 
the  virtual  image  O'  whereas  the  object  is  at  0.  The  fore- 
going principles  of  reflection  and  refraction  are  made  use  of 
in  the  Weldon  Range  Finder,  which  may  now  be  better  under- 
stood. 

The  Weldon  Range  Finder  is  a small  hand  instrument  for 
use  in  measuring  ranges,  a full  description  of  which  is  published 
in  pamphlet  form  by  the  Ordnance  Department. 

The  main  feature  of  the  instrument  is  a combination  of 
three  small  flat  triangular  prisms  assembled  one  above  the 
other  with  their  principal  sections  parallel  to  each  other. 


222 


GUNNERY 


If  we  erect  a right-angle  triangle  (Fig.  9)  with  a base  1/50 
of  the  altitude,  the  other  two  angles  will  be  88°  51'  15"  and 
1°  9'  45". 

And  if  we  erect  an  obtuse-angle  triangle,  (Figure  10),  with 
an  angle  of  91°  8'  45"  included  between  two  sides,  one  four 
times  as  long  as  the  other,  the  other  two  angles  of  the  tri- 
angle will  be  74°  43'  15"  and  13°  58'.^ 

The  first  prism  of  the  Weldon  Range  Finder  is  so  arranged 
as  to  reflect  an  angle  of  90°.  In  other  words,  it  deflects  the 
virtual  image  through  a right  angle. 

Hence,  if  the  observer  at  the  B.  C.  Station  holds  the  prism 
in  a vertical  position  the  object  (Figure  11)  appears  in  the 

o' 


Fig.  11. 


direction  BO'  instead  of  at  0.  Knowing  that  this  prism  is 
made  to  reflect  an  angle  of  90°,  he  is  able  to  lay  off  a perpen- 
dicular to  BO  by  marking  the  direction  BO'. 

The  second  prism  reflects  an  angle  of  88°  51'  15". 

Therefore,  if  the  observer,  using  this  prism,  moves  back- 
ward to  I (Figure  12)  where  he  brings  the  virtual  image  O' 
into  coincidence  with  B or  any  point  on  a line  drawn  from  B 
perpendicular  to  BO,  the  distance  BI  will  be  1/50  of  BO  or 
the  range. 

^ There  are  360“  in  a circle,  60'  (minutes)  in  a degree  and  60"  (seconds) 
in  a minute.  Angles,  as  we  know,  are  measured  in  degrees.  Minutes  and 
seconds  are  simply  fractions  of  a degree. 


RANGE  AND  RANGING 


223 


The  third  prism  reflects  an  angle  of  74°  53'  15". 
Therefore,  if  the  observer  using  the  prism,  moving  back- 
ward to  I (Figure  13),  brings  the  virtual  image  into  coincidence 
with  B,  he  knows  that  he  is  i as  far  from  B as  O is  from  B. 


o' 


With  a full  understanding  of  the  foregoing,  the  various 
methods  of  necessary  ranges  as  set  forth  by  the  Ordnance 
Department  in  the  Range  Finder  Pamphlet  should  appear 
very  simple. 

The  discussion  of  the  laws  of  reflection  and  refraction  will 


serve  to  impress  upon  the  mind  the  absolute  necessity  of  hold- 
ing the  prisms  in  a vertical  position  to  attain  any  degree  of 
accuracy  in  determining  the  range.  It  also  explains  the  move- 
ments of  the  virtual  image. 


CHAPTER  IV 


ANGLE  OF  SITE 


Fig.  1. 


We  have  seen  that  the  angle  of  sight  in  ballistics  is  the 
angle  between  the  line  of  sight  and  the  horizontal.  The  angle 
of  site  in  practical  gunnery  is  the  same  as  the  angle  of  sight. 
If  the  definition  of  the  word  site  be  borne  in  mind,  there  should 
be  no  difficulty  with  the  angle  of  site.  The  site  of  an  object 
is  its  position,  location,  or  situation.  One  object  may  be 
situated  either  higher  or  lower  than  another,  or  at  the  same 
elevation.  Therefore,  the  site  of  a target  may  be  at  a higher 

or  lower  elevation  than 
that  of  the  guns  and  the 
B.  C.  station,  and  the 
site  of  the  latter  may  be 
higher  or  lower  than  the 
site  of  the  target  and  the 
battery,  or  they  may  all 
three  be  at  the  same 
level.  The  elevation  of  the  site  of  the  target  "with  respect  to 
the  guns  must  be  accurately  determined  and  the  angle  made 
by  a straight  line  from  the  site  of  the  target  to  the  right  gun 
with  the  horizontal  is  the  angle  of  site. 

Suppose  a gun  were  located  at  G (Fig.  1)  and  that  the 
ranges  to  the  fort  F and  work  W were  the  same.  If  the  range 
merely  were  given,  the  trajectory  would  be  GP,  with  point  of 
impact  at  P.  Neither  the  fort  nor  the  work  would  be  struck 
although  the  projectile  had  sufficient  range  to  hit  either. 

Now  if  the  piece  were  so  elevated  that  the  trajectorj^  passed 
through  F,  the  range  being  the  same,  the  straight  line  from  the 
target  to  the  piece  would  make  the  angle  / with  the  horizontal. 

A.  S.  of  F=f 

f is  positive  (+)  because  an  angle  of  elevation. 

224 


ANGLE  OF  SITE 


225 


If  the  piece  were  so  depressed  that  the  trajectory  passed 
through  W,  the  range  being  the  same,  the  straight  line  from  the 
target  to  the  piece  would  make  the  angle  w with  the  horizontal. 


Fig.  2. 


A.  S.  of  W=w 

w is  negative  ( — ) because  an  angle  of  depression. 

The  quadrant  on  the  gun  is  so  arranged  that  when  the 
target  is  on  the  same  level  with  the  gun  the  trajectory  will 
pass  through  the  j 

target,  no  matter 
what  the  range, 
when  the  instru- 
ment is  set  at  300 
mils.  The  normal  angle  of  site  then  is  300.  For  all  readings 
less  than  300  the  gun  is  depressed,  and  for  all  over  it  is  ele- 
vated, after  the  piece  is  set  for  the  proper  range. 

If  the  piece  were  fired  (Fig.  2)  with  A.  S.  300,  when  the 
gun  was  below  the  target,  the  projectile  would  strike  at  Ti, 
some  distance  below  the  target  T.  If  the  line  GT  be  taken  to 
represent  the  surface  of  the  ground  the  actual  point  of  impact 
would  be  X. 

And  so,  if  the  piece  were  fired  with  A.  S.  300,  when  the 
target  was  below  the  gun,  the  projectile  would  strike  at  T' 

(Fig.  3)  above  the 
target,  resulting  in 
a very  high  burst. 

Angle  of  site  is 
easily  determined. 
If  the  range  is 
3,000  yds.  each  mil  subtends  3 yds.  Suppose  the  target 
(Fig.  4)  is  63  feet  above  the  guns.  63  ft.  = 21  yds.  = 7 mils. 

If  the  target  is  7 mils  above  the  guns  A.  S.  = 307. 

The  elevation  in  mils  of  any  point  can  be  read  direct  with 
the  B.  C.  telescope.  If  the  site  of  the  point  is  higher  than  the 
station  the  reading  is  300  + the  elevation;  if  lower  the  reading 
is  300  — the  depression. 


Fig.  3. 


226 


GUNNERY 


Suppose,  from  the  station  B,  the  reading  of  the  telescope 
for  T is  330  mils  and  for  G is  200  mils.  The  range  of  T is 
3,000  yds.  and  each  mil  subtends  3 yds.  Therefore  T is  30X3 
= 90  yds.  or  180  ft.  above  B. 

The  distance  of  G from  B is  200  yds.  Each  mil  subtends 
2 yds.  Therefore  G is  100  X .2  = 20  yds.  or  60  feet  below  B. 


If  G is  60  feet  below  B and  T is  180  feet  above  B,  T is 
180  + 60  = 240  feet  above  G. 

The  problem  now  is  to  compute  the  proper  A.  S.  for  G 
so  that  the  trajectory  will  pass  through  T.  Taking  3,000  yds. 
as  the  range  (G  may  be  on  a line  with  B instead  of  straight 
behind),  1 mil  subtends  3 yds.  or  9 feet.  It  will  take  240  9 

= 26§  or  27  mils  elevation  or  an  A.  S.  of  327  for  the  guns  to 
hit  T. 

Now  suppose  (Fig.  5)  the  B.  C.  station  is  higher  than  both 
the  guns  and  the  target. 

The  telescope  reading  for  the  site  of  the  target  is  270  mils. 


There  is  a depression  then  of  30  mils.  At  4,000  yds.  30  mils 
= 4 X 30  yds.  = 360  feet. 

The  reading  for  the  site  of  the  guns  is  150  mils.  There  is 
a depression  then  of  150  mils.  At  300  yds.  each  mil  = .3  yd. 
and  100  X .3  yd.  = 30  yds.  or  90  feet. 


ANGLE  OF  SITE 


227 


It  is  obvious  then  if  T is  360  feet  below  B,  and  G is  90 
feet  below  B,  that  T is  270  feet  below  G. 

270  feet  = 90  yds. 

1 mil  at  4,000  yds.  = 4 yds. 

Then  T is  90-^4  = 22.5  mils  below  G,  or 
A.  S.  = 300 -22.5  = 277.5. 

By  means  of  the  foregoing  solution  we  arrive  at  a general 
formula  for  the  calculation  of  angle  of  site  from  the  B.  C. 
station  which  is  as  follows: — 


If  values  be  substituted  in  this  formula  the  result  will  be 
the  same  obtained  before.  All  distances  must  be  in  yds.  and 
depressions  must  be  given  negative  values  ( — ).  The  solu- 
tion then  with  the  formula  is  as  follows: — 


Lg  = level  of  gun  Lt  = level  of  target 

R = range  300  = Normal  Reading. 


Lg  = 90  feet  = 30  yds.  = — 30 

Lg  = 360  feet  = 120  yds.  = — 120 
R = 4,000  yds.  = 4,000. 


A.  S.  = 300- 


/ -30-(-120)\^  /-30+120\ 

I 4,000  V 4 / 

\ 1,000  J 


\4/ 

A.  S.  = 277.5 


228 


GUNNERY 


The  importance  of  accurately  determining  the  angle  of 
site  is  illustrated  by  Figs.  6 and  7.  In  Figure  6 the  target  is  at 
T but  an  error  in  the  angle  of  site  (a)  causes  the  trajectory  to 
pass  through  GT'X  instead  of  to  T,  GT'  being  same  curve  as 
GT.  The  effect  in  this  case  is  to  lengthen  the  range  to  the 


extent  of  TX,  which  upsets  all  calculations  for  corrector  as  we 
shall  see  later. 

Let  us  suppose  the  first  salvo  (Fig.  6)  results  in  high  bursts 
at  T'.  If  the  corrector  were  lowered  the  bursts  would  occur 
along  the  trajectory  toward  X and  all  beyond  the  target. 
Suppose  the  original  corrector  were  retained  and  the  range 
shortened  in  the  effort  to  get  a 1-mil  height  of  burst.  The 
bursts  would  recede  toward  G and  a burst  might  be  secured 
at  some  such  point  as  b that  would  be  effective.  It  would  be 
too  high  for  the  best  results,  however,  and  in  the  meantime 


there  has  been  a useless  waste  of  ammunition  and  possibly  a 
disclosure  of  position. 

If  the  error  is  one  of  depression  the  result  is  even  more  dis- 
astrous. 

Let  a,  Fig.  7,  represent  the  error  in  angle  of  site  and  sup- 
pose that  the  trajectory  passes  through  the  points  GxTi  to 


ANGLE  OF  SITE 


229 


Ti,  a point  below  the  target  T.  Impact  would  occur  at  a:  if 
the  line  GT  is  the  surface  of  the  ground.  Hence  we  would 
get  a burst  on  graze  until  the  corrector  had  been  raised  to 
draw  the  burst  past  the  point  x of  the  trajectory.  This  so 
shortens  the  range  as  to  make  the  projectile  ineffective. 

The  effects  of  the  errors  are  greatly  exaggerated  in  the 
figures.  The  nature  of  the  effect  from  such  errors,  however,  is 
more  forcibly  impressed  upon  the  mind.  Very  slight  errors 
would  cause  perhaps  no  appreciable  loss  of  effect  from  shrap- 
nel. 

At  medium  ranges  a change  of  4 mils  in  the  angle  of  site 
produces  a change  of  about  100  yds.  in  range.  If  the  angle  of 
site  used  is  too  great  the  range  is  increased,  and  if  the  error 
is  the  other  way  it  is  shortened. 

It  must  be  constantly  borne  in  mind  that  error  in  angle  of 
site  lengthens  or  shortens  the  range,  and  causes  bursts  on 
graze  or  too  high  bursts  and  bursts  beyond  the  target. 


CHAPTER  V 


CORRECTOR 

Let  GOT  (Figure  1)  be  the  trajectory  for  the  range  GT. 
The  perpendicular  OiO  to  the  highest  point  of  the  trajectory 
is  the  maximum  ordinate  of  the  trajectory.  Angle  d is  the 
angle  of  departure  and  angle  / is  the  angle  of  fall. 


If  the  fuze  is  set  for  the  range  GT  by  means  of  the  fuze 
setter,  theoretically  the  projectile  would  burst  at  T,  and  a 
burst  on  graze  would  result;  from  the  very  nature  of  shrapnel 
the  effect  of  the  projectile  would  be  in  a great  measure  lost. 
Now  if  the  conditions  of  the  atmosphere  were  such  that  the 
powder  train  of  the  fuze  burned  more  rapidly  than  under  nor- 
mal conditions,  or  if  the  fuze  were  so  defective  as  to  cause  the 
bursting  charge  to  explode  prematurely  or  before  the  projec- 
tile reached  T,  the  burst  could  only  occur  at  some  point  on 
the  trajectory.  The  highest  point  at  which  it  could  explode 
would  be  0.  Under  normal  conditions  then,  with  the  fuze  set 
for  a given  range,  the  projectile  would  burst  at  the  point  of 
impact  or  at  T.  The  fire  with  shrapnel  would  be  practically 
ineffective,  as  it  has  not  the  power  of  impact  which  an  explo- 
sive shell  has  and  yet  there  would  be  no  dispersion  of  pellets, 
the  very  object  for  which  the  shrapnel  is  designed. 

230 


CORRECTOR 


231 


In  order  to  secure  the  desired  result  a device  is  attached  to 
the  fuze  setter  by  means  of  which  the  fuze  may  be  so  shortened 
as  to  cause  the  projectile  to  burst  at  a point  where  the  maxi- 
mum effect  from  the  dispersion  of  the  pellets  will  be  had  upon 
the  target.  In  other  words  the  fuze  is  altered  or  corrected. 

Let  GT'T  (Fig.  2)  be  the  trajectory  for  the  range  GT.  It 
has  been  found  by  tests  that  the  maximum  effect  upon  T 
will  be  secured  when  the  shrapnel  bursts  in  front  of  and  about 
3 mils  higher  than  the  target.  Therefore,  the  fuze  is  corrected 
so  as  to  cause  explosion  at  T',  3 mils  above  T.  The  normal 
correction  then  causes  a three-mil  height  of  burst.  On  the 
corrector  scale  attached  to  the  fuze  setter  the  normal  correc- 


tion is  marked  30,  the  scale  running  from  0 to  60.  Every 
point  below  the  normal  lowers  the  burst  one  mil  and  every 
point  above  30  elevates  the  burst  one  mil  on  the  trajectory. 
It  is  obvious  that  the  course  of  the  projectile  is  not  altered,  for 
the  trajectory  is  determined  by  the  elevation  of  the  piece. 
Nothing  that  could  be  done  with  the  fuze  would  change  the 
elevation  of  the  piece,  and  however  short  the  fuze  is  set  the 
projectile  cannot  burst  higher  than  its  trajectory. 

In  determining  the  range  of  a target  it  is  obviously  neces- 
sary to  burst  the  projectile  as  near  T as  possible,  for  the  puff 
of  smoke  resulting  from  the  explosion  is  the  indicator  or  flag 
which  is  waved  in  front  of  or  behind  the  target,  signaling  the 
error  in  the  range.  If  the  signal  is  given  right  at  the  target 
the  accuracy  of  the  range  is  easily  observed,  for  the  flag  or 
puff  either  obscures  or  is  partially  obscured  by  the  target, 
whereas  if  the  puff  occurs  in  front  of  and  above  the  objective, 
as  it  does  at  the  normal  height  of  burst,  it  is  difficult  to  tell 


232 


GUNNERY 


whether  a high  burst,  however  effective  it  may  be,  is  just 
beyond,  immediately  over,  or  at  the  proper  interval  short. 
Hence  in  ranging,  or  in  adjusting  the  fire,  instead  of  the 
normal  corrector  which  gives  a 3-mil  height  of  burst,  a cor- 
rector 2 points  lower  is  used  to  secure  a 1-mil  height  of  burst. 
If  the  range  and  the  angle  of  site  are  absolutely  correct,  the 
fuze  perfect,  and  atmospheric  conditions  normal,  corrector  30 
gives  a mean  or  average  height  of  burst  of  3 mils,  and  corrector 
28  a one-mil  height  of  burst.  If,  however,  conditions  are  such 
that  a 1-mil  height  of  burst  is  secured  with  corrector  30,  then 
32  gives  the  3-mil  height  of  burst  and  32  will  have  to  be  em- 
ployed instead  of  30  in  firing  for  effect. 

Now,  if  the  mean  height  of  burst  is  adjusted  by  trial  shots 
at  one  range  the  same  corrector  is  used  for  other  ranges,  pro- 
vided no  error  in  angle  of  site  is  made  for  the  latter.  Of  course 


the  bursts  will  be  higher  for  longer  ranges  as  the  lineal  value 
of  the  mil  in  the  vertical  plane  increases  with  the  range.  Thus, 
at  3,000  yards  the  mean  height  of  burst  is  3 X 3 yards  = 27  feet ; 
and  at  4,000  yards  it  is  3X4  yards  = 36  feet.  And  so  a mean 
height  of  burst  of  1 mil  for  these  ranges  would  be  9 feet  and  12 
feet  respectively.  (Figure  3.) 

It  is  seen  then  that  an  increase  of  n mils  in  the  corrector 
setting  makes  a corresponding  increase  of  n mils  in  the  height 
of  burst;  a decrease  of  n mils  in  the  corrector  setting  makes  a 
corresponding  decrease  of  n mils  in  the  height  of  burst. 

The  height  of  any  particular  burst  may  be  measured  by 
means  of  the  B.  C.  telescope.  The  mean  height  of  a salvo 
may  also  be  estimated  with  considerable  accuracy,  if  the  bm-sts 
as  they  occur  are  noted  with  respect  to  the  horizontal  lines  in 


CORRECTOR 


233 


the  field  of  view  of  the  telescope,  and  an  average  is  then  made. 
The  middle  line  indicates  the  normal  height  of  burst;  the  upper 
line  twice  the  normal  height. 

The  observer  must  also  be  trained  to  estimate  by  eye  the 
height  of  a single  burst  or  the  mean  height  of  a salvo. 

When  the  mean  point  of  burst  is  at  the  height  appropriate 
during  the  adjustment  (1  mil),  from  one-half  to  one-fourth 
of  the  shrapnel  may,  on  account  of  the  error  of  the  fuse,  be 
expected  to  burst  on  graze.  Similarly,  when  the  mean  point 
of  burst  is  at  the  height  appropriate  during  fire  for  effect 
(3  mils),  about  one-tenth  may  be  expected  to  burst  on 
graze. 

A check  is  thus  afforded  on  the  adjustment  of  the  height 
of  burst,  provided  a considerable  number  of  rounds  fired  with 
the  same  fuze-setting  are  observed. 

In  the  accurate  adjustment  of  time  fire  not  only  the  height 
but  also  the  interval  of  burst  is  important;  for  projectiles 
bursting  too  far  in  front  of  the  target  and  those  bursting  in  the 
air  above  it  produce  little  or  no  effect.  The  interval  of  burst 
is  correct  when  both  the  range  and  the  height  of  burst  are 
correctly  adjusted.  Indications  that  such  is  the  case  are:  (1) 
That  the  bursts  on  graze  bracket  the  target;  (2)  that  a due 
proportion  of  the  projectiles  burst  on  graze;  (3)  that  the  mean 
height  of  burst  is  about  3 mils;  (4)  that  fragments  from  the 
time  bursts  strike  the  ground  both  in  front  and  rear  of  the 
target,  and  that  the  pattern  made  by  these  fragments  (as 
revealed  by  the  dirt  and  dust  knocked  up)  is  close  and  dense 
rather  than  greatly  extended;  (5)  that  obvious  effect  is  pro- 
duced upon  the  target. 

If  doubt  exists  as  to  the  interval  of  burst  it  is  best  to  dimin- 
ish the  corrector  and  get  a group  of  low  bursts  and  bursts  on 
graze. 

Observers  posted  well  to  the  flank  of  the  line  of  fire  may  be 
of  the  greatest  assistance  in  determining  and  correcting  errors 
in  the  interval  of  burst. 


234 


GUNNERY 


Suppose,  then,  in  an  adjusting  salvo  at  3,000  yards  there  are 
one  burst  on  graze  and  three  bursts  in  air  as  follows: — 40  ft., 
50  ft.,  and  30  ft.  high  respectively.  The  average  or  mean 
height  of  burst  is  40+50+304-3=120-^40  feet,  or  13  yards. 
A mil  at  3,000  yds.  is  3 yds.  and  a mean  height  of  burst  of 
between  4 and  5 mils  instead  of  1 mil  has  been  secured.  There- 
fore, if  corrector  v/as  28,  for  first  salvo,  we  should  next  use  a 
corrector  3 points  less  or  25.  Now  suppose  a salvo  gives  2 
bursts  10  ft.  in  air  and  2 on  graze;  the  mean  height  of  burst 
is  correct  (about  1 mil),  the  fire  is  adjusted,  and  the  corrector 


for  the  fire  for  effect  should  be  increased  to  27,  which  will  give 
a mean  height  of  burst  of  3 mils  or  9 yds.  or  27  feet. 

An  error  in  the  angle  of  site,  as  we  have  seen,  affects  the 
range  to  the  extent  of  about  100  yds.  for  every  4 mils  of 
error.  It,  therefore,  interferes  with  the  accurate  and  prompt 
adjustment  of  the  height  of  burst  in  proportion  to  the  amount 
of  the  error. 

The  influence  of  the  error  is  illustrated  by  Fig.  4.  Let  us 
assume  that  the  objective  is  not  in  the  same  horizontal  plane 
as  the  gun,  but  is  at  O',  the  range  being  the  same  for  0 and  O'. 
In  order  to  make  the  trajectory  pass  through  O'  it  is  necessarj’- 
to  increase  the  elevation  of  the  piece  by  the  angle  of  site  O'GO. 

Now  if  the  range  GO'  = GO  the  range  ring  on  the  fuze 
setter  is  not  changed,  since  it  must  correspond  to  the  range. 

The  same  corrector  which  would  give  a 3 -mil  brnst  at  B 
would  with  the  change  in  angle  of  site  give  a burst  at  B',  for 
the  burst  will  occur  at  the  same  point  on  the  trajectory  no 


CORRECTOR 


235 


matter  through  what  angle  the  trajectory  may  have  been 
revolved.  (See  rigidity  of  trajectory:  Exterior  Balhstics.) 
Hence  the  angle  B'GO'  = the  angle  BGO;  which  means  that 
B'0'  = B0. 

Let  us  assume  that  the  corrector  gives  a burst  B (Fig.  5) 
at  a height  of  3 mils  above  0,  situated  in  the  horizontal  plane. 
The  trajectory  is  then  GBO.  Suppose  the  objective  is  at  O', 
at  the  same  distance  as  O,  but  15  mils  above  the  horizontal 
plane.  Let  us  assume  that  the  angle  of  sight  O'GO  is  neglected. 


The  burst  would  occur  at  B much  too  low  since  B'  is  the  point 
3 mils  above  O'.  The  burst  must  therefore  be  raised  through 
the  angle  BGB';  that  is,  the  corrector  must  be  increased  by 
the  number  of  mils  contained  in  this  angle. 

Now  BGB'  = OGO'  since  B'GO'  and  BGO  are  both  equal 
to  3 mils.  Hence  BGB'==  15  mils  or  the  error  in  the  angle  of 
site.  As  a consequence  of  this  he  must  raise  his  corrector  15 
mils,  the  exact  amount  by  which  he  decreased  the  angle 
of  site,  the  target  being  taken  at  0 instead  of  15  mils  above 
at  O'. 

A course  of  reasoning  exactly  identical  would  show  that 
for  an  objective  situated,  for  example,  10  mils  below  the  hori- 
zontal plane,  if  an  angle  of  site  too  great  by  10  mils  is  used, 
the  corrector  will  have  to  be  lowered  by  10  mils. 

The  practical  results  of  an  error  in  the  angle  of  site  are 
now  easily  perceived.  To  determine  the  sense  of  a round,  the 
projectile  is  made  to  burst  1 mil  above  the  ground,  so  that  the 
smoke  of  the  burst  will  either  obscure  the  target  or  be  obscured 


236 


GUNNERY 


by  it.  Corrector  28,  under  normal  conditions,  will  give  a 
mean  height  of  burst  of  1 mil. 

If  the  angle  of  site  used  is  greater  than  the  true  angle  or  in 
error  by  too  much  elevation,  the  bursts  of  the  first  adjusting 
salvo  with  corrector  28  will  be  too  high  and  it  will  be  impos- 
sible to  judge  its  sense  accurately.  If  the  error  in  angle  of 
site  is  an  error  in  elevation  of  15  mils  the  bursts  will  be  16 
mils  above  the  target  instead  of  1 mil  above.  Now  if  the  cor- 
rections are  too  timid,  it  will  take  many  rounds  to  determine 


the  sense  of  a salvo  or  of  a trial  shot  and  the  adjustment  of 
the  range  will  therefore  be  delayed. 

Now  if  the  error  in  the  angle  of  site  is  one  of  depression, 
that  is,  if  the  muzzle  of  the  piece  be  depressed  too  much,  bursts 
on  impact  will  result  at  the  point  where  the  trajectory  meets 
the  surface  of  the  ground. 

T is  the  actual  position  of  the  target  (Fig.  6),  the  dotted 
line  GET  the  trajectory  at  the  proper  angle  of  site  and  B 
the  proper  point  of  burst.  The  angle  a is  the  error  of  depres- 
sion and  Bi  the  point  of  impact.  If  GT  is  the  surface  of 
the  ground,  the  projectile  would  never  reach  a point  3 mils 
above  T. 

The  limitations  upon  the  elevation  of  burst  by  raising  the 
corrector  are  apparent.  The  burst  cannot  be  secured  at  a 
point  higher  than  the  trajectory.  Hence  a large  error  in  the 
angle  of  site  cannot  be  compensated  for  by  corrector.  Thus 
in  Fig.  6 it  is  readily  seen  that,  even  if  a burst  were  secured 
on  the  trajectory  GBiTi,  by  raising  the  corrector  so  as  to  draw 


CORRECTOR 


237 


the  burst  above  Bi,  the  projectile  would  have  no  effect  on  the 
target  T if  the  distance  BiT  were  greater  than  the  depth  of 
the  cone  of  dispersion. 

Generally  speaking,  when  error  in  angle  of  site  is  present, 
the  cause  of  the  error  in  height  of  burst  is  not  at  first  known. 
If  the  error  in  angle  of  site  is  small  the  height  of  burst  may  be 
readily  adjusted,  but  if  the  necessary  correction  exceeds  the 
limit  of  the  corrector  scale,  then  the  total  correction  which  has 
been  applied  to  the  corrector  must  be  transferred  in  the  same 
sense,  that  is,  added  to  the  angle  of  site  if  30  + and  subtracted 
from  the  angle  of  site  if  30 — , and  the  fire  continued  with  the 
new  angle  of  site  and  with  a corrector  about  normal. 

Suppose,  for  instance,  fire  was  opened  with  angle  of  site 
300  and  corrector  28;  after  continuous  corrections  of  5 
points  up  to  corrector  48  still  no  burst  in  air  is  secured.  A 
correction  of  20  points  has  been  made.  Add  the  total  cor- 
rection to  the  angle  of  site  employed.  Then  continue  to 
adjust,  commencing  with  angle  of  site  320  and  corrector  28. 

In  the  same  way,  if  angle  of  site  is  280  and  the  bursts  are 
all  on  graze  after  a total  correction  downward  of  10  points, 
the  angle  of  site  should  be  changed  to  270  and  corrector  28 
employed  to  commence  again. 

Now  let  us  suppose  no  burst  in  air  has  been  obtained  with 
corrector  40  and  angle  of  site  290.  Add  12  to  the  angle  of 
site,  which  gives  a new  angle  of  site  of  302,  and  use  corrector 
28,  which  is  40  — 12. 

There  are  authorities  which  hold  that  the  corrector  should 
be  applied  as  soon  as  the  error  in  angle  of  site  is  detected,  as 
above,  whether  the  adjustment  may  be  had  through  the  use 
of  the  corrector  or  not.  Others  claim  that  compensation  for 
error  in  angle  of  site  by  change  of  corrector  up  to  the  limit  is 
admissible.  The  former  have  the  argument  in  their  favor 
that  with  the  true  angle  of  site  the  fire  is  normal,  whereas  in 
the  latter  case  an  abnormality  exists  with  respect  to  the  tra- 
jectory, which  does  not  pass  through  the  target  as  it  should. 


238 


GUNNERY 


When  the  trajectory  passes  through  the  target,  relative  changes 
in  range  and  in  angle  of  site  may  be  made,  and  the  normal  cor- 
rector used,  whereas  when  adjustment  has  been  secured  by 
abnormal  corrections  of  the  height  of  burst,  relative  changes  in 
range  and  in  angle  of  site  are  impracticable.  This  disadvan- 
tage increases  with  the  correction.  When  the  correction  is 
small  the  disadvantage  is  of  no  practical  effect. 


CHAPTER  VI 


OBSERVATION  OF  FIRE 

The  time  required  to  adjust,  in  order  to  secure  an  effective 
fire,  and  the  expenditure  of  ammunition  may  both  be  greatly 
reduced,  if,  by  reconnaissance,  the  enemy’s  positions  are  well 
determined  and  if,  by  auxiliary  observers  pushed  well  to  the 
front  and  flank,  information  is  obtained  which  will  assist  in 
the  adjustment  of  fire. 

The  searching  of  areas  is  never  to  be  resorted  to  unless  it 
can  be  definitely  determined  that  the  enemy  is  actually  located 
within  the  area  selected,  and  unless  he  would  evidently  exer- 
cise a material  influence  upon  the  progress  of  the  combat  if 
left  undisturbed  by  fire. 

The  officer  conducting  the  fire  should  be  posted  where  he 
can  observe  not  only  his  immediate  target,  but  as  much  as 
possible  of  the  terrain  liable  to  be  assigned  him  to  attack. 
Unembarrassed  by  details  of  the  service  of  the  guns  he  should 
devote  himself  to  observing  and  correcting  the  fire  and  adapt- 
ing its  employment  to  meet  the  requirements  of  the  situation. 
He  should  train  himself  to  form  accurate  and  quick  estimates 
and  to  act  on  them  with  decision  and  boldness. 

To  overlook  ground  which  is  visible  to  the  officer  conducting 
the  fire,  as  well  as  for  the  purpose  of  assisting  generally  in  the 
adjustment  of  fire,  free  use  is  to  be  made  of  auxiliary  observing 
parties. 

Such  parties  occupy  the  most  favorable  observing  stations 
which  the  conditions  of  the  combat  admit.  Preferably  they 
are  as  near  the  enemy  as  possible.  If  near  the  guns,  they  are 
posted  usually  on  the  flanks  and  in  elevated  positions,  if  pos- 
sible; for  example,  in  the  tops  of  trees,  on  buildings,  on  arti- 
ficial towers,  etc. 


239 


240 


GUNNERY 


Their  special  duties  are  to  signal  information  which  will 
assist  in  the  adjustment  of  fire  and  to  keep  the  artillery  com- 
mander informed  of  movements  of  the  targets  or  of  our  own 
troops  which  would  affect  the  employment  of  fire. 

With  respect  to  the  adjustment  of  fire,  they  indicate  espe- 
cially whether  the  range  is  short,  over,  or  correct,  whether  the 
interval  of  burst  (distance  of  point  of  burst  in  front  of  target) 
is  too  great,  too  small,  or  correct;  whether  the  direction  is 
right,  left,  or  correct. 

If  large  errors  in  range  are  made,  an  observer  on  the  flank 
of  the  guns  will  not  usually  be  able  to  separate  the  errors  in 
range  from  those  in  direction;  in  such  a case  the  observer 
would  ordinarily  signal  the  direction  only,  as  right  or  left,  as 
it  appears  to  him,  and  the  officer  conducting  the  fire,  knowing 
the  position  of  the  observer,  would  deduce  the  sense  of  the 
salvo,  volley,  etc.,  in  range.  If  the  observer  is  to  the  right  of 
the  line  of  fire,  shots  striking  short  of  the  target  appear  to  be 
to  the  left,  while  those  striking  over  appear  to  be  to  the  right, 
and  vice  versa  if  he  is  on  the  left  of  the  line  of  fire. 

With  respect  to  movements  of  the  enemy,  the  observer 
reports  especially:  If  the  enemy  abandons  his  position;  if 
he  shifts  to  the  right  or  left,  front  or  rear,  to  escape  effective 
fire;  if  additional  hostile  troops  enter  the  sector  assigned  the 
guns. 

With  respect  to  our  own  troops,  the  observer  makes  such 
reports  as  to  their  movements  and  situation  as  will  enable 
the  artillery  commander  to  best  assist  them  with  the  fire  of 
the  guns. 

Arrangements  should,  moreover,  be  made  with  advanced 
troops  of  the  other  arms  for  the  transmission  of  informa- 
tion which  will  assist  in  the  adjustment  of  fire  and  for  the 
indication  as  to  when  fire  should  be  commenced  or  discon- 
tinued. 

Sure  and  definite  means  of  communication  must  be  estab- 
lished between  the  artillery  commander,  his  observing  parties. 


OBSERVATION  OF  FIRE 


241 


and  advanced  friendly  troops.  If  time  admits,  telephone 
communication  is  provided;  but  visual  signaling  must  always 
be  relied  upon  to  a greater  or  less  extent. 

For  observation  of  fire,  for  study  of  the  terrain,  and  for 
the  quick  recognition  of  objectives,  good  field  glasses  are 
indispensable.  All  officers  of  the  artillery,  chiefs  of  section, 
and  scouts  must  be  equipped  with  suitable  glasses. 

At  the  commencement  of  the  fire  it  is  usually  best  to  watch 
for  the  burst  of  the  shots  with  the  unaided  eyes,  for  if  a large 
error  is  made  the  burst  may  not  appear  in  the  field  of  view  of 
a telescope  or  field  glass.  After  the  bursts  have  been  located 
the  glasses  may  be  quickly  brought  into  play,  if  necessary,  and 
the  relative  position  of  the  smoke  with  respect  to  the  target 
noted. 

Alter  the  fire  has  been  approximately  adjusted  the  points 
of  burst  are  observed  by  the  aid  of  field  glasses  or  the  tele- 
scope, and  all  the  indications  carefully  noted  which  assist  in 
the  determination  of  their  relative  positions  with  respect  to 
the  target. 

Much  ingenuity  may  be  employed  in  observation  in  general. 
Before  any  system  can  be  effective,  however,  a definite  set  of 
signals  or  means  of  communication  must  be  established.  It 
is  surprising  how  often  a word  or  a movement  of  the  arm 
will  convey  an  entirely  different  meaning  from  the  one  in- 
tended. 

Two  approved  methods  of  lateral  observation  are  here 
given,  the  first  when  two  observers  are  employed;  the  second 
when  a single  observer  is  used. 

1.  The  case  of  two  observers  D.  and  K.,  Figure  1.  Each 
observer  (at  night  each  should  use  two  lanterns)  faces  the 
battery  while  at  the  same  time  observing  the  target.  Each 
of  them  extends  his  right  arm  if  the  shot  appears  to  him  to  the 
right  of  the  target,  and  his  left  arm  if  the  shot  appears  to  him 
to  the  left;  both  arms  if  the  shot  appears  to  him  correct  in 
direction. 


242 


GUNNERY 


Assume  that  OL  is  the  target. 

Short  Shots  Included  in  the  Zone  KLOD. 

Each  shot  in  the  angle  KAD  is  to  the  left  for  D,  to  the  right 

for  K.  Both  extend  the  arm  away 
from  the  target. 

Any  shot  in  the  triangle  KLA  is 
to  the  left  for  D,  in  line  for  K.  The 
observer  K extends  both  arms;  the 
observer  D extends  the  arm  away 
from  the  target. 

Any  shot  in  the  triangle  DAO 
is  in  line  for  D,  to  the  right  for  K. 
D extends  both  arms;  K extends  the 
arm  away  from  the  target.  Thus, 
when  both  observers  extend  an  arm 
in  the  direction  away  from  the 
target,  or  when  one  extends  both 
arms  in  that  direction  and  the  other 
extends  one  arm,  the  shot  is  short. 
Shots  That  Are  Over  and  Included  in  the  Zone  FLOI. 

Any  shot  in  the  angle  GBH  is  to  the  right  for  D,  to  the 
left  for  K.  Both  extend  the  arm  toward  the  target. 

Any  shot  in  the  zone  FLBG  is  in  line  for  D,  to  the  left 
for  K.  D extends  both  arms;  K extends  the  arm  toward  the 
target. 

Any  shot  in  the  zone  HBOI  is  to  the  right  for  D,  in  line 
for  K.  K extends  both  arms;  D extends  the  arm  toward  the 
target.  Thus,  when  both  observers  extend  an  arm  toward 
the  target,  or  when  one  extends  both  arms  and  the  other 
extends  the  arm  toward  the  target,  the  shot  is  over. 

Shots  Near  the  Target. 

Any  shot  in  quadrilateral  ALBO  is  in  line  for  both  D 
and  K.  Both  extend  both  arms. 


OBSERVATION  OF  FIRE 


243 


Doubtful  Shots. 

Any  shot  in  the  angle  DOI  is  to  the  right  for  D,  to  the 
right  for  K.  One  extends  the  arm  toward  the  target;  the  other 
extends  the  arm  away  from  the 
target.  It  is  the  same  if  the  shot 
bursts  in  the  angle  KLF. 

Thus,  when  both  observers 
extend  the  arm,  one  toward  the 
target  and  the  other  in  a direc- 
tion away  from  the  target,  the 
shot  is  doubtful. 

To  sum  up : The  shot  is  over 
when  both  observers  extend  the 
arm  toward  the  target,  or  when 
one  extends  both  arms  and  the 
other  extends  the  arm  toward 
the  target. 

The  shot  is  short  when  both 
observers  extend  the  arm  away 
from  the  target,  or  when  one  extends  both  arms  and  the  other 
extends  the  arm  away  from  the  target. 

The  shot  is  near  when  both  observers  extend  both  arms. 

The  shot  is  doubtful  when  one  extends  the  arm  toward  the 
target  and  the  other  in  the  opposite  direction. 

2.  The  case  of  a single  observer.  (Fig.  2): 

The  captain  is  at  C. 

Short  Shots  Included  in  the  Zone  CLOD. 

Any  shot  in  the  angle  CAD  is  to  the  right  for  the  captain, 
to  the  left  for  the  observer  D.  D extends  the  arm  away  from 
the  target. 

Any  shot  in  the  angle  CAL  is  in  line  for  the  captain,  to 
the  left  for  D.  D extends  the  arm  away  from  the  target. 

Any  shot  in  the  angle  DAO  is  to  the  right  for  the  captain, 
to  the  right  for  D.  D extends  both  arms. 


Fig.  2. 


244 


GUNNERY 


Thus,  when  the  observation  of  the  captain  does  not  agree 
with  that  of  the  observer  D,  the  shot  is  short  if  he  extends  the 
arm  away  from  the  target;  it  is  also  short  if,  D extending  both 
arms,  the  shot  is  to  the  right  for  the  captain. 

Shots  Over  and  Included  in  the  Zone  FLOI. 

Any  shot  in  the  angle  GBH  is  to  the  left  for  the  captain, 
to  the  right  for  D.  D extends  the  arm  toward  the  target. 

Any  shot  in  the  zone  FLBG  is  to  the  left  for  the  cap- 
tain, in  line  for  D.  D extends  both  arms. 

Any  shot  in  the  zone  HBOI  is  in  line  for  the  captain,  to 
the  right  for  D.  D extends  the  arm  toward  the  target. 

Thus,  when  the  observation  of  the  captain  does  not  agree 
with  that  of  the  observer  D,  the  shot  is  over  if  he  extends  the 
arm  toward  the  target ; it  is  also  over  if,  D extending  both  arms, 
the  shot  is  to  the  left  for  the  captain. 

Shots  Close  to  the  Target. 

Any  shot  in  the  quadrilateral  ALBO  is  in  line  for  the 
captain,  in  line  for  D. 

Doubtful  Shots. — Any  shot  in  the  angle  DOI  is  to  the 
right  for  the  captain;  to  the  right  for  D. 

Any  shot  in  the  angle  CLF  is  to  the  left  for  the  captain;  to 
the  left  for  D. 

To  sum  up:  Whenever  the  observation  of  the  captain 
does  not  agree  with  that  of  the  observer  the  shot  is  over  if 
the  observer  extends  the  arm  toward  the  target;  it  is  short 
if  the  observer  extends  the  arm  away  from  the  target. 

If  the  observer  extends  both  arms,  the  shot  is  over  if  it  is 
to  the  left  for  the  captain;  the  shot  is  short  if  it  is  to  the  right 
for  the  captain. 

If  the  observer  extends  both  arms  the  shot  is  close  to  the 
target  if  it  is  in  line  for  the  captain. 

There  is  no  doubt  if,  the  shot  not  being  in  line,  the  obser- 
vation of  the  captain  agrees  with  that  of  the  observ^er. 


CHAPTER  VII 


POSITION  AND  THE  MASK 

Positions  are  defined  as  masked  or  unmasked,  according  as 
they  afford  concealment  or  not. 

When  no  concealment  is  afforded  the  guns  are  said  to  be 
in  an  unmasked  'position,  and  the  fire  is  referred  to  as  unmasked 
fire. 

When  concealment  is  afforded  the  guns  are  said  to  be  in  a 
masked  position  and  the  fire  is  referred  to  as  masked  fire. 

The  mask,  then,  is  the  intervening  object  which  screens  the 
guns  from  the  view  of  the  enemy. 

If  the  guns  are  posted  behind  a mask  in  such  position  that 
the  hostile  position,  or  the  target,  may  be  seen  through  the 
sights,  they  are  said  to  have  sight  defilade. 

If  they  are  posted  where  a dismounted  man  can  just  see 
the  target  over  the  mask,  they  are  said  to  have  dismounted 
defilade. 

If  where  a mounted  man  can  just  see  the  target  over  the 
mask,  to  have  mounted  defilade. 

If  so  that  the  flash  of  the  guns  will  be  concealed,  to  have 
flash  defilade. 

While  the  drill  regulations  give  12  feet  below  the  crest  of 
the  mask  as  the  point  of  flash  defilade,  in  practice  20  feet  is 
more  satisfactory. 

A mask  can  either  be  a mere  screen,  such  as  a fringe  of 
trees,  or  a hedge,  enabling  direct  laying  to  be  employed,  or  it 
may  be  such  a natural  object  as  a hillside,  or  a dense  thicket, 
entailing  the  necessity  of  indirect  fire.  In  the  first  case  the 
projectile  passes  through  the  mask,  in  the  latter  the  tra- 

245 


246 


GUNNERY 


jectory  must  clear  the  obstacle.  It  would  perhaps  be  better 
if  concealment  of  the  former  character  were  strictly  defined 
as  a screen,  the  latter  only  being  referred  to  as  a mask,  for 
the  distinction  is  important.  If  fire  is  merely  referred  to  as 
masked,  we  do  not  necessarily  know  whether  it  is  direct  or 
indirect.  Therefore,  we  should  designate  the  fire  either  as 
direct  fire  masked  or  indirect  fire,  in  order  to  convey  an  exact 
meaning. 

Practicability  of  the  Mask. — Much  has  been  wTitten,  and 
grave  doubts  are  entertained,  about  the  practicability  of  the 
mask  in  actual  service.  Question  is  raised,  of  course,  more  par- 
ticularly with  respect  to  masked  fire  against  infantry. 

In  advancing  against  another  body  at  a distance  of  some 
thousands  of  yards  over  ground  exposed  to  artillery  fire,  infan- 
try takes  its  precautions  accordingly,  usually  assuming  a 
formation  in  small  groups — say  from  a platoon  to  half  a dozen 
men.  These  groups,  often  several  hundred  yards  apart, 
advance  by  rapid  rushes  of  varying  length.  The  Japanese 
groups  are  known  to  have  advanced  continuously  for  four 
hundred  yards  at  amazing  speed  before  lying  down,  a perform- 
ance quite  beyond  the  endurance  of  European  troops  in  gen- 
eral. In  view,  then,  of  the  unstationary,  shifting  character 
of  the  infantry  as  a target,  much  uncertainty  exists,  especially 
in  the  ranks  of  the  infantry  and  cavalry,  as  to  whether  artil- 
lery fire  is  sufficiently  flexible  to  repel  an  infantry  assault  when 
indirect  laying  is  employed.  While  the  Japanese  doubt  was 
confirmed  by  their  experiences  in  the  fighting  around  Liao 
Yang,  we  must  remember  that  the  guns  there  used  were  not 
comparable  in  efficiency  with  those  with  which  the  French, 
English,  and  our  own  artillery  are  now  equipped. 

The  French  system  of  fire  against  infantry  seems  to  be 
more  flexible  than  any  other,  because  of  the  highly  independent 
employment  of  individual  guns,  a single  gun  only  being  used 
to  fire  upon  a small  group,  an  appropriate  target  for  the  weapon. 
The  danger  of  a less  independent  use  of  the  guns  in  repelling 


POSITION  AND  THE  MASK 


247 


an  infantry  assault  is  the  tendency  of  the  battery  commander 
to  wait  for  an  opening  to  use  the  four  guns  effectively,  whereas 
such  an  opportunity  may  never  present  itself,  or,  if  it  did,  it 
might  not  be  until  late  in  the  action  when  the  two  infantries 
were  in  close  contact.  Yet  indirect  fire  against  rapidly 
advancing  infantry  does  not  seem  to  be  contemplated  even 
in  the  French  system. 

The  artilleryman  observing  groups  of  approaching  infan- 
try will  notice  that  they  generally  come  into  sight  at  particu- 
lar points  indicated  by  the  nature  of  the  terrain — woods, 
hedges,  sunken  roads,  hills,  etc. — and,  further,  that  such  of 
these  bits  of  cover  as  form  the  longest  salients  toward  him  seem 
the  most  popular.  “Infantry  like  electricity,”  says  Major 
Buat,  “has  a tendency  to  escape  from  points.”  It  will  also 
be  observed  that  the  current  of  groups  flowing  from  any  par- 
ticular bit  of  cover  directs  itself  upon  another.  Between 
the  two  bits  of  cover  each  group  advances  by  short  rushes; 
behind  it  are  other  groups,  some  in  motion,  some  stationary, 
but  all  transitory. 

If  we  now  add  that  all  these  streams  of  groups  take  their 
origin  at  varying  distances  from  the  observer — for  the  patches 
are  scattered  irregularly  over  the  ground — we  shall  have  a 
fairly  good  idea  of  the  target  presented  to  the  battery,  a target 
more  or  less  difficult  for  direct  fire.  “It  is  evident,”  says 
Major  Buat,  “that  all  the  batteries  in  an  army  corps  would 
not  go  far  if  we  should  try  to  assign  one  to  look  after  every 
stream  of  groups,  or  even  every  two  or  three  streams.  Out  of 
all  the  batteries  thus  brought  into  action,  only  a few  guns  at 
a time  would  be  usefully  employed.  The  rest  would  be  firing 
upon  unoccupied  ground,  or  not  firing  at  all.  All  this  leads  us 
to  try  to  economize  both  guns  and  ammunition,  and  to  use  a 
few  guns  working  actively  instead  of  a large  number  firing 
slowly  and  intermittently.  One  gun  should  be  enough  to  fire 
upon  a target  of  a squad  or  two.  This  is  practically  impossible 
except  with  direct  fire.  Can  we  conceive  of  anything  more 


248 


GUNNERY 


difficult,  and  more  impractical,  than  a battalion,  or  a battery 
commander,  calmly  perched  upon  an  observing  station  or 
tower,  indicating  the  data  for  a large  number  of  guns  firing 
upon  numberless  small  groups  moving  at  a rapid  rate,  and 
frequently  disappearing  altogether?  Indeed,  before  the  data 
could  be  transmitted,  and  the  pieces  layed,  new  data  would  be 
required.” 

Based  upon  the  foregoing  considerations,  and  what  has 
actually  been  seen  at  maneuvers,  the  principal  objections  urged 
against  indirect  lajdng  are  as  follows: — 

1.  The  tendency  of  field  artillery  officers  to  seek  the  masked 
position,  regardless  of  the  tactical  situation  and  of  the  end  that 
the  guns  are  called  upon  to  accomplish. 

2.  The  delay  in  occupying  positions  and  in  opening  fire, 
caused  by  the  time  taken  up  in  making  preliminary  reconnais- 
sance and  in  computing  the  elements  of  fire. 

The  foregoing  objections  cannot  be  more  ably  answered 
than  they  have  been  by  Colonel  McMahon  in  a recent  article 
to  which  the  student  is  referred.* 

As  regards  the  first  objection,  it  may  be  said  that  the 
excessive  use  of  cover  in  maneuvers  is,  in  the  general  case, 
caused  by  the  fear  of  the  artillery  commander  that  he  will  be 
harshly  criticized  by  the  umpires  for  unnecessary  exposures 
of  his  command,  and  that  he  will  be  charged  up  with  losses 
which,  fortunately  for  all  those  who  bear  arms,  occur  onlj'  when 
blank  ammunition  is  used.  The  slowness  may  be  attributed 
to  various  causes,  lack  of  proper  training  of  the  personnel, 
failure  to  keep  in  proper  adjustment  the  instruments  for  the 
conduct  and  observation  of  fire,  failure  to  maintain  proper 
communication  between  the  officer  conducting  the  fire  and  the 
firing  unit,  and,  lastly,  the  tendency,  which  fortunately  is  now 
rapidly  disappearing,  to  make  use  of  coast  artillery  methods 

*Col.  John  E.  McMahon,  G.  S.  C.,  Infantry  Journal,  July-August,  1911, 
^‘Concerning  Masked  Fire.”  See  author’s  article  “Concerning  Masks,”  Field 
Artillery  Journal,  January,  1912. 


POSITION  AND  THE  MASK 


249 


in  the  determination  of  firing  data,  with  a consequent  sacri- 
fice of  the  essential  properties  of  the  rapid-fire  field  gun.  How- 
ever just  these  criticisms  may  be,  it  should  be  noted  that  the 
objections  urged  against  the  use  of  masked  fire  in  general  are 
not  inherent  in  the  system  itself,  but  can  be  easily  overcome 
by  proper  instruction  and  training.  The  fact  also  remains 
that,  unless  the  doubts  as  to  the  practicability  of  masked  fire 
be  removed  from  the  minds  of  infantry  and  cavalry  officers, 
when  war  breaks  out  the  field  artillery  will  find  itself  at  vari- 
ance with  the  other  branches  of  the  mobile  army,  and  the  coop- 
eration so  essential  to  success  will  be  entirely  lacking.  To 
clear  up,  if  possible,  this  atmosphere  of  doubt  is  the  writer’s 
object. 

Paragraph  690,  Field  Artillery  Drill  Regulations,  1908, 
states : 

“TO  POST  THE  GUNS  SO  AS  TO  BE  ABLE  TO 
CARRY  OUT  EFFECTIVELY  THE  TASK  ASSIGNED 
IS  ALWAYS  THE  FIRST  CONSIDERATION  IN  THE 
SELECTION  OF  A POSITION.” 

Again,  paragraph  698  says: 

“When  it  is  necessary  to  bring  guns  into  action  quickly 
for  the  support  of  other  troops,  the  main  consideration  is  to 
get  them  as  promptly  as  possible  to  a place  from  which  they 
can  render  effective  support.  In  such  a case,  delay  occasioned 
by  the  search  for  technical  and  tactical  advantages  is  entirely 
inadmissible.” 

From  this  it  appears  that  in  our  field  artillery  system  the 
use  of  masked  positions  is  plainly  made  dependent  on  the 
tactical  situation  and  the  purpose  that  the  guns  are  called 
upon  to  perform;  and  that  the  artillery  commander  who  seeks 
cover  at  the  expense  of  fire  efficiency  is  acting  in  direct  oppo- 
sition to  the  spirit  of  the  regulations.  On  the  other  hand,  the 
artillery  officer  who,  from  a spirit  of  bravado  or  a failure 
properly  to  estimate  the  tactical  situation,  needlessly  exposes 
his  guns  in  the  open  runs  great  risk  of  bringing  disaster  upon 


250 


GUNNERY 


the  troops  with  which  he  is  serving  and  at  the  same  time  sacri- 
fices uselessly  one  of  the  most  important  properties  of  the  rapid- 
fire  field  gun — the  power  of  acting  by  surprise. 

It  may  be  fairly  stated  that,  under  the  limitations  given 
above,  in  all  engagements  of  any  importance  except  combats 
of  cavalry  against  cavahy,  the  modern  tendency  is  to  make 
masked  fire  the  normal  method  of  procedure.  The  French, 
who  were  the  pioneers  in  all  that  pertains  to  modern  field 
artillery,  have  lately  had  their  drill  regulations  revised  by  a 
commission  made  up  of  their  ablest  officers  of  that  arm.  This 
commission  has  laid  down  three  great  principles  governing  the 
employment  of  field  artillery  in  battle,  and  the  first  of  these 
principles  is,  ‘‘Artillery  will  preferably  occupy  masked  posi- 
tions.” The  Germans,  who  sought  for  a long  time  to  cover  up 
their  deficiencies  in  material  by  a pretended  contempt  for  the 
French  methods  and  stoutly  maintained  the  advantages  of 
the  “partially  exposed  positions,”  are  to-day  prevented  from 
acknowledging  the  truth  of  the  French  principles  only  by 
lack  of  funds  to  purchase  the  accessories  that  make  effective 
masked  fire  possible.  The  infantry  officer  should  therefore 
be  prepared  to  face  the  fixe  of  guns  that  he  does  not  see  and  to 
allow  the  artillery  commander  the  necessary  freedom  to  decide 
whether  or  not  the  tactical  situation  demands  the  placing  of 
the  artillery  in  the  open. 

It  is  not  expected  that  the  reader  will  take  for  granted  the 
dictum  that  in  the  general  case  the  masked  position  is  to  be 
preferably  sought.  The  advantages  claimed  for  it  are  the 
following : 

1.  Without  sacrificing  any  of  its  offensive  properties,  artil- 
lery in  a masked  position  can  escape  destruction  and  at  the 
same  time  preserve  its  liberty  of  action.  TMiile  the  cannoneers 
of  a modern  field  battery  are  protected  from  shrapnel  and 
infantry  fire  by  shields,  the  officers  and  chiefs  of  section  must 
necessarily  be  exposed  in  the  performance  of  their  respective 
duties.  The  supply  of  ammunition  must  also  be  affected  in 


POSITION  AND  THE  MASK 


251 


the  open.  It  is  therefore  certain  that  a battery  exposed  in 
the  open  to  weU-adjusted  artillery  fire  will  find  its  effective- 
ness seriously  compromised  by  grave  losses  among  its  officers 
and  non-commissioned  officers  and  by  the  great  difficulty 
experienced  in  bringing  up  ammunition  from  the  combat  train. 
It  cannot  bring  up  its  horses  to  move  the  guns  to  a more  shel- 
tered position  without  risking  annihilation.  At  the  Yalu 
three  Russian  batteries  posted  in  the  first  line  attempted  to 
retire  before  the  Japanese  advance.  The  guns  had  been 
placed  in  advance  of  the  military  crest  and  the  limbers  had  to 
cross  the  crest  to  reach  the  guns.  Their  losses  from  the  Jap- 


anese  artillery  were  as  follows: 

Officers. 

Men. 

Horses. 

2nd  Battery,  6th  Division .... 

....  7 

79 

108 

3rd  Battery,  6th  Division .... 

. . . . 1 

23 

74 

3rd  Battery,  3rd  Division 

5 

86 

72 

— 

— 

— 

Total 

....  13 

188 

254 

The  only  recourse  for  a battery  exposed  in  the  open  to 
effective  fire  from  the  enemy’s  guns  in  a covered  position  is 
to  cease  firing,  shelter  its  personnel,  and  wait  for  an  oppor- 
tunity to  reopen  fire  when  its  adversaries  have  been  forced 
to  transfer  their  attention  to  another  target  by  the  intervention 
of  a friendly  battery.  A battery  thus  pinned  to  the  ground  is 
exposed  to  the  added  danger  of  having  its  material  destroyed 
by  high-explosive  shell  fire.  Against  this  projectile  the  shields 
are  helpless,  and  experiment  has  proven  that,  up  to  ranges  of 
3,000  yds.,  the  battery  that  is  forced  to  stand  idle  in  an  exposed 
position  under  effective  shrapnel  fire  will  promptly  be  reduced 
to  scrap  iron,  if  attacked  by  well-adjusted  shell  fire. 

2.  A battery  in  a masked  position  can  prepare  its  fire  in 
advance,  thereby  reaping  the  full  advantage  of  its  character- 
istic property  of  being  able  to  act  by  surprise.  Under  the 
protection  of  the  covering  crest,  the  battery  commander  recon- 


252 


GUNNERY 


noiters  and  occupies  the  position  quietly  and  coolly,  undis- 
turbed by  the  fire  of  the  hostile  guns.  He  can  register  in 
advance  the  zone  assigned  to  hun,  prepare  the  firing  data  for 
the  prominent  objects  in  the  zone  and  thus  be  ready  to  open 
fire  quickly  against  the  targets  appearing  in  his  front.  By  a 
skillful  selection  of  the  emplacement  of  his  guns,  he  can  deceive 
the  enemy  as  to  his  distance  from  the  crest,  and  so  force  him 
to  consume  much  ammunition  in  the  attempt  to  locate  the 
position  of  the  guns.  If  he  finds  that  his  adversary  is  approach- 
ing the  correct  adjustment  in  range  and  direction,  he  can  tempo- 
orarily  cease  firing,  thus  causing  the  enemy  to  beheve  that 
adjustment  has  been  secured  and  to  open  his  fire  for  effect 
before  the  elements  of  fire  have  been  correctly  determined. 
If  ordered  to  change  position  he  can  do  so  without  incurring 
serious  losses  among  his  men  and  horses. 

3.  When  indirect  laying  is  used,  artillery  fire  can  be  not 
only  directed  upon  a target  but  also  shifted  to  a new  objective 
more  quickly  and  effectively  than  when  direct  laying  is  em- 
ployed. Based  upon  target  ground  experiences,  in  which  a single 
objective  appears  at  a time  and  the  firing  is  conducted  under 
favorable  circumstances,  this  may  seem  a startling  statement 
to  make.  Let  us  assume  that  artillery  has  taken  a position 
in  the  open  and  has  been  assigned  a sector  of  the  battle  front. 
A target  suddenly  appears  in  that  sector  and  it  becomes  neces- 
sary for  the  battery  commander  to  point  it  out  definitel}'  to 
his  four  gunners,  a task  easy  enough  in  the  quiet  atmosphere 
of  the  target  ground,  but  quite  another  matter  in  the  roar  and 
confusion  of  battle.  In  some  cases  he  wall  have  to  assemble 
his  chiefs  of  section  and  gunners  in  order  that  he  may  make 
sure  that  the  target  is  identified.  The  proper  distribution  of 
the  fire  of  the  battery,  so  that  the  fire  of  each  gun  may  be 
directed  upon  its  proper  section  of  the  target,  must  be  left  to 
the  platoon  commanders.  Should  a new  objective  appear, 
the  same  difficulties  are  renewed.  If  the  battery  were  using 
indirect  laying  the  problem  would  be  much  simplified.  Before 


POSITION  AND  THE  MASK 


253 


disclosing  his  position,  the  battery  commander  selects  as 
registration  marks  a number  of  prominent  objects  in  the  sector 
assigned  him  and  prepares  in  advance  the  elements  of  fire  for 
these  points.  As  each  new  target  appears  he  loses  no  time  in 
attempting  to  point  it  out  to  the  gunners.  He  simply  com- 
mands for  example:  “Add  80,”  or  “Subtract  120,”  correcting 
the  deflection  previously  used  by  the  angular  distance  between 
the  new  objective  and  the  registration  mark  or  the  target  upon 
which  the  guns  were  last  laid.  By  proper  changes  in  the 
deflection  difference  he  can  obtain  converging  or  parallel  fire, 
and  can  open  and  close  the  sheaf  at  will.  In  this  way  the 
chances  of  error  are  greatly  decreased  and  much  time  is 
saved — the  latter  a most  important  consideration  when  we 
remember  the  fleeting  nature  of  the  targets  that  will  in  general 
be  presented  to  the  artillery  on  the  battlefield. 

Turning  to  the  other  side  of  the  question,  the  main  objections 
urged  against  indirect  laying  from  a covered  position  are  that 
this  method  requires  too  much  time  for  the  delivery  of  fire; 
that  it  causes  a dead  space  in  front  of  the  covering  crest,  the 
extent  of  which  depends  on  the  degree  of  defilade  assumed; 
and  that  it  entails  the  separation  of  the  battery  commander 
from  his  battery,  with  a consequent  loss  of  control  over  his 
men. 

As  to  the  first  objection,  it  may  be  said  that  indirect  laying 
should  not  be  used  whenever  there  is  necessity  for  a quick 
entry  of  the  guns  into  action.  Artillery  brought  up,  for  exam- 
ple, to  drive  back  a menacing  attack  already  under  way 
should  not  waste  valuable  time  in  an  endeavor  to  secure  cover. 
In  cavalry  combats,  again,  the  open  position  and  direct  fire 
will  be  the  rule.  It  is  only  when  the  tactical  situation  permits 
a careful  and  deliberate  preparation  of  fire — and  this  will 
be  the  case  seven  out  of  ten  times  in  an  engagement  of 
any  magnitude — that  the  covered  position  will  be  used. 
Even  when  so  used,  there  is  no  good  reason  why  the 
opening  of  fire  should  be  unduly  delayed.  The  time 


254 


GUNNERY 


required  is  a direct  function  of  the  training  of  the 
personnel.  It  may  be  safely  said  that  a skillful  battery 
commander  should  be  ready  to  begin  his  fire  within  five  minutes 
after  his  guns  are  in  position.  The  day  for  elaborate  calcu- 
lations and  careful  measurements  of  angles  has  gone  by. 
The  parallax  method  for  computing  the  firing  data  is  suffi- 
ciently accurate  for  use  in  the  great  majority  of  cases.  It  is 
devoutly  to  be  hoped  that  when  the  next  war  comes  the  spec- 
tacle will  not  be  seen  of  a battery  commander  sitting  down 
behind  the  sheltering  crest  with  pad  and  pencil  in  hand,  pon- 
dering over  the  question  whether  n is  plus  or  minus,  while  the 
infantry  is  lying  in  the  open  anxiously  waiting  for  the  sight  of 
the  shrapnel  bursting  over  the  enemy’s  lines. 

The  objection  as  to  the  dead  space  is  a more  serious  one. 
In  considering  the  subject,  however,  it  should  be  remembered 
that  generally  the  artillery  will  be  posted  in  rear  of  the  line 
occupied  by  the  infantry,  and  that,  consequently,  they  will 
be  able  to  cover  the  ground  in  front  of  the  infantry  position, 
even  though  a dead  space  exist  in  front  of  the  guns.  This 
dead  space,  moreover,  is  not  so  serious  an  objection  in  the 
case  of  artillery  supporting  an  attack  as  it  would  be  in  a defen- 
sive position.  Skillful  dispersion  of  the  guns,  by  which  the 
dead  space  in  front  of  one  battery  may  be  swept  by  the  fire 
of  another  posted  on  the  flank,  will  help  to  solve  the  problem. 
The  fire  of  heavy  field  howitzers  will  be  especially  useful  for 
this  purpose.  The  dead  space  may  be  reduced  in  extent  by 
occupying  the  front  slope  of  a second  crest,  and  may  be  par- 
tially swept  by  firing  at  the  minimum  range  possible  for  a 
given  position  with  a high  corrector,  thus  causing  the  shrapnel 
to  burst  short  and  high,  but  the  efficiency  of  the  projectile 
will  be  considerably  reduced  by  this  method.  The  disadvan- 
tages of  the  dead  space  may  also  be  reduced  by  the  skillful 
battery  commander  who,  when  making  his  preliminary  recon- 
naissance, first  determines  the  minimum  range  at  which  he 
will  probably  be  called  upon  to  fire  and  then  selects  the  degree 


POSITION  AND  THE  MASK 


255 


of  defilade  to  correspond  to  this  condition.  For  example,  if 
the  tactical  conditions  are  such  that  he  may  reasonably  expect 
that  the  necessity  will  arise  for  him  to  completely  sweep  the 
front  slope  of  the  covering  crest,  he  will  take  a position  of 
either  dismounted  or  sight  defilade  and  move  the  guns  up  by 
hand  when  the  critical  moment  arrives,  as  was  done  years 
ago  at  Gettysburg  and  Fredericksburg. 

The  separation  of  the  battery  commander  from  his  battery 
may  possibly  affect  the  morale  of  the  men,  but  with  the  excel- 
lent field  telephone  now  supplied  the  field  artillery  the  can- 
noneers at  the  guns  are  always  practically  within  sound  of 
their  “master’s  voice.”  As  a matter  of  fact,  this  objection  is 
one  based  principally  on  peace  conditions;  for  in  time  of  war  the 
limited  space  assigned  the  field  artillery  of  a large  army  will 
not  permit  the  battery  commander  to  place  his  observation 
station  at  such  distances  from  the  battery  as  is  possible  on  a 
target  range.  Resort  will  be  had  to  observation  towers,  or  to 
natural  objects  in  the  vicinity  of  the  guns,  from  which  a clear 
view  of  the  ground  in  front  may  be  obtained. 

As  to  the  question  whether  masked  fire  is  really  practicable, 
there  can  be  but  one  answer  for  the  field  artilleryman  to  make. 
This  question  was  settled  once  for  all  in  the  Manchurian  war. 
The  Japanese,  even  though  without  a long-recoil  gun  or  any 
of  the  standard  instruments  that  now  form  an  essential  part 
of  the  equipment  of  a battery,  were  nevertheless  able  to  fire 
from  masked  positions  with  such  effect  as  to  overpower 
the  Russian  guns,  at  first  habitually  fought  in  the  open. 
With  the  excellent  instruments  for  the  conduct  and  observa- 
tion of  fiire  now  furnished  our  field  artillery,  effective  fire 
from  a covered  position  is  merely  a matter  of  proper  train- 
ing. The  infantry  may  rest  assured  that  the  material  is  all 
right  and  that  the  personnel  is  seeking  by  every  means  in 
its  power  to  reach  that  stage  of  efficiency  which  will  make 
the  field  artillery  the  strong  right  arm  of  the  infantry  in 
battle. 


256 


GUNNERY 


Position. — An  artillery  “position”  does  not  necessarily 
mean  a defensible  feature  of  the  ground.  It  merely  means  the 
place  where  the  guns  come  into  action,  and  may  be  anything 
from  a sunken  road  or  a corn  field  to  a commanding  ridge. 

It  is  most  desirable  that  the  guns  should  stand  on  firm  and 
level  ground,  free  from  large  stones.  Unless  the  ground  is 
firm  the  spade  will  not  take  hold  properly,  and  the  gun  vail 
tend  to  jolt  sideways  during  firing. 

If  the  ground  slopes  down  to  the  front  it  is  often  impossible 
to  get  sufficient  elevation  at  the  first  round,  before  the  spade 
is  imbedded,  especially  when  the  target  is  above  the  gun. 

If  the  gun  be  on  a steep  reverse  slope,  firing  at  a low  angle 
of  elevation,  then  the  axis  of  the  piece  will  make  a larger  angle 
with  the  trail  and  the  gun  will  jump  instead  of  remaining  steady 
on  firing. 

Large  boulders  and  a rocky  sod  prevent  the  spade  from 
taking  a fair  bearing,  and  make  the  gun  exceedingly  difficult 
to  traverse.  The  B.  C.  must  give  the  ground  of  the  position 
much  the  same  consideration  that  a mariner  gives  to  his 
anchorage,  that  is — will  the  anchor  hold. 

Whenever  the  anchorage,  so  to  speak,  is  bad,  it  will  be 
found  to  save  time  if  the  section  commanders  and  gunners  are 
permitted  to  select  emplacements  for  their  pieces  before  the 
battery  is  brought  into  action. 

Direct  Fire. — Since  the  command  of  a position  must  be 
good,  the  guns  are  usually  posted  on  high  ground.  The  choice 
of  a position  for  direct  fire  will  as  a rule  he  between  the  for- 
ward crest  and  the  rear  crest  or  between  the  military  crest 
and  the  actual  crest. 

In  the  accompanying  figure,  the  military  crest  is  at  IM,  the 
actual  crest  at  C,  and  the  rear  crest  at  R.  The  mihtarj'  crest 
may  therefore  be  said  to  be  the  point  of  slope  from  which  the 
greatest  command  of  the  foreground,  including  the  underlying 
terrain,  may  be  had,  while  the  actual  crest  is  at  the  skyline, 
and  the  rear  crest  is  in  rear  of  and  below  the  sky-line. 


POSITION  AND  THE  MASK 


257 


All  of  the  space  from  M to  0 is  defiladed  against  fire 
from  C and  is  therefore  called  dead  space  with  respect  to  the 
actual  crest. 

The  forward  or  military  crest  position  gives  a better  view, 
and  the  guns,  being  below  the  sky  line,  are  difficult  for  the 
enemy  to  locate,  so  long  as  the  men  keep  still.  On  the  other 
hand,  the  forward  position  renders  ammunition  supply  difficult 
and  with  the  3-inch  gun,  which  has  a long  trail  vuth  a large  spade 
at  the  end  of  it,  it  is  often  impossible  to  get  sufficient  elevation 


for  the  first  round  vuthout  digging  a small  trench  for  the  spade. 
When  this  is  the  case  and  there  is  no  time  for  trenching,  it  is  some- 
times advisable  to  fire  the  first  round  with  as  much  elevation 
as  possible  even  if  insufficient  to  reach  the  target,  if  by  so 
doing  the  spade  will  be  sufficiently  imbedded  to  give  the  neces- 
sary elevation. 

As  a rule,  the  forward  crest  position  makes  it  easier  for 
the  enemy  to  get  the  range  of  the  guns,  since  the  sense  of  rang- 
ing shots  can  be  easily  determined. 

The  rear  crest  position  has  the  serious  drawback  that 
the  guns  must  stand  above  the  sky  line,  and  also  that  the 
field  of  view  and  the  field  of  fire  are  both  inferior  to  that 
obtained  from  the  forward  crest.  The  former  disadvantage 
may  be  minimized  by  keeping  the  guns  run  back  until  required 
to  open  fire;  while  the  latter  may  be  somewhat  minimized 
in  so  far  as  view  is  concerned  by  keeping  lookout  men  with 
glasses  in  front  of  each  flank.  The  field  of  fire,  of  course,  can- 
not be  increased  to  any  great  extent  by  running  the  guns  for- 
ward. There  will  always  be  a large  dead  space  just  below  the 


258 


GUNNERY 


military  crest  which  the  guns  cannot  search  whether  posted 
on  the  rear  or  on  the  actual  crest.  It  will  be  recalled  that 
Bragg  so  posted  his  artillery  at  Lookout  Mountain  and  that 
Sherman’s  and  Sheridan’s  infantry  were  able  to  reach  the 
guns  without  suffering  very  greatly  from  their  fire. 

The  slope  of  descent  of  a shell  at  3,000  yards  is  about  1 
in  6;  that  of  the  lower  bullets  of  a shrapnel  is  about  1 in  5. 
Now  a hill  with  a slope  as  steep  as  1 in  5 from  top  to  bottom  is 
rarely  to  be  met  with.  It  follows  that  it  is  practically  impos- 
sible to  obtain  cover  for  the  limbers  and  wagons  by  posting 
them  at  the  foot  of  the  hill  close  behind  the  guns. 

Since  many  of  the  shell  fired  at  the  guns  will  burst  quite  200 
yards  over,  and  since  the  shrapnel  bullets  are  effective  300 
yards  beyond  the  point  of  burst,  it  follows  that  the  line  of 
limbers  and  teams  must  be  at  least  500  yards  distant  if  placed 
in  rear  of  the  guns,  or  still  further  if  the  enemy’s  range  is 
short.  It  is  sufficiently  obvious  that  it  is  not  desirable  to 
place  the  limbers  and  teams  and  the  reserve  in  rear  of  the  bat- 
tery under  any  circumstances  if  it  can  be  avoided,  for  if  thej’’ 
are  far  enough  to  the  rear  to  be  safe  from  hostile  fire  they  are 
too  far  away  to  permit  of  celerity  in  the  change  of  position. 
The  same  consideration,  of  course,  which  renders  the  placing 
of  the  limbers  in  rear  of  their  own  guns  undesirable  holds 
true  with  respect  to  the  placing  of  the  limbers  in  rear  of  other 
batteries  on  the  flanks  of  the  battery  to  which  they  belong. 
If  the  line  of  guns  constituting  the  group  is  a very  extended  one, 
however,  it  will  be  necessary  to  place  the  limbers  of  an  interior 
battery  in  the  rear  of  some  of  the  guns.  In  such  a case  good 
judgment  as  to  the  best  protection  available  must  be  employed. 

Alignment  of  Guns. — There  is  one  other  point  which  may 
be  noted  here,  for  it  applies  to  every  position  which  guns  occupy 
where  there  are  several  in  line.  It  is  sometimes  thought,  and 
possibly  in  one  respect  with  justice,  that  exact  drill  and  dress- 
ing are  of  but  little  importance  nowadaj^s  to  artilleiy,  or  that, 
at  any  rate,  too  much  attention  has  been  hitherto  paid  to  them. 


POSITION  AND  THE  MASK 


259 


In  order,  however,  to  ensure  that  the  full  activity  of  every  gun 
shall  be  available  for  every  emergency,  it  is  desirable  that  they 
take  up  a precise  alignment;  otherwise  it  may  happen  that 
when  fire  has  to  be  turned  to  a flank  some  of  the  guns  may  mask 
or  at  least  interfere  with  the  fire  of  others.  Thus,  if  several 
guns  be  drawn  up  upon  an  uneven  or  slightly  curved  line,  and 
it  should  be  necessary  to  shift  the  sheaf  of  the  battery  through 
a considerable  angle  to  the  right  or  left,  a gun  in  the  center,  if 
too  far  advanced,  may  mask  the  fire  of  those  on  the  flanks. 
Similarly,  if  the  line  of  guns  be  curved  inwardly,  those  in  the 
center  may  find  their  fire  interfered  with  by  those  that  are 
more  advanced.  These  considerations  are  of  even  more  impor- 
tance in  connection  with  the  batteries  of  a battalion. 

To  facilitate  ranging,  it  is  desirable  that  the  correct  inter- 
vals betv/een  guns  and  batteries  be  observed.  The  crest  line 
of  the  height  occupied  should  also  run,  if  possible,  at  right 
angles  to  the  proposed  line  of  fire;  otherwise  the  position  may 
be  enfiladed  from  some  position  of  the  enemy  other  than  that 
being  fired  upon. 

When  it  is  impossible  to  find  a suitable  position  at  right 
angles  to  the  line  of  fire,  it  must  be  considered  whether  it  is 
better  for  all  the  pieces  brought  into  action  at  a particular 
position  to  be  echeloned  along  the  crest  line  affording  the  posi- 
tion, or  whether  the  batteries  should  be  placed  at  right  angles 
to  the  line  of  fire,  and  themselves  as  units  be  in  echelon  while 
their  guns  are  in  line. 

Entrenchments. — In  entrenching  a gun,  the  first  thing  to 
see  to  is  that  its  fire  can  be  directed  upon  any  target  in  the 
sector  of  fire.  If  an  epaulment  or  a gun  pit  is  used,  there  must 
be  sufl&cient  space  to  permit  a full  traverse  of  the  gun. 

Protection  for  the  detachment  is  best  provided  by  digging 
deep  trenches  on  either  side  of  the  gun,  in  which  the  men, 
when  not  actually  serving  the  gun,  can  sit  with  their  backs  to 
the  parapets,  their  heads  being  at  least  a foot  below  the 
crest,  which  must  be  thick  and  solid.  It  must  be  remembered 


260 


GUNNERY 


that  the  angle  of  descent  of  shrapnel  bullets,  at  medium  ranges, 
is  about  1 to  5,  so  that  protection  is  only  obtainable  close  under 
the  parapet,  unless  overhead  cover  can  be  constructed.  On 
no  account  must  cover  be  constructed  on  the  sky  hne  or  actual 
crest.  The  best  position  for  gun  entrenchments  is  usually 
the  military  crest.  Epaulments  and  gun  pits,  or  the  guns 
themselves  when  unprotected,  should  be  obscured  by  brush, 
and  the  natural  features  of  the  ground  should  always  be  taken 
advantage  of  when  possible,  even  if  the  prescribed  spacing  of 
the  guns  has  to  be  disregarded.  Of  course,  the  intervals 
cannot  be  so  largely  increased  as  to  render  the  calculations  for 
deflection  impractical  except  for  the  right  piece. 

With  ten  gunners  digging,  and  three  drivers  cutting  sods, 
and  hauling  them  on  the  limbers  when  necessary,  it  takes  from 
three  to  four  hours  to  provide  good  cover  for  a gun,  or  double 
this  time  to  construct  overhead  cover,  provided  timber  is 
handy. 

If  dummy  entrenchments  are  constructed  within  the  ene- 
my’s view  so  as  to  divert  the  fire  from  the  true  position  of  the 
guns  they  should  be  at  such  a distance  from  the  latter  that  the 
effect  of  inaccurate  and  wild  shots  will  not  be  felt.  Under 
service  conditions,  at  medium  ranges,  the  total  rectangle  of  a 
fire  directed  at  the  dummy  entrenchments  would  be  about 
500  yards  by  100  yards.  The  dummies  should,  therefore,  be 
at  least  100  yards  from  the  guns. 

The  Russians  and  Boers  both  made  frequent  use  of  the 
device  of  a double  set  of  entrenchments  for  their  guns  and 
groups  of  guns.  When  the  fire  of  the  enemy  became  well 
adjusted,  the  guns  were  simply  withdrawn  to  the  second  set 
of  entrenchments,  without  the  rectangle  of  hostile  fire,  no 
change  being  apparent  to  the  enemy  in  the  point  from  which 
they  received  the  fire  of  the  guns  they  were  firing  upon.  Ham- 
ilton, as  well  as  the  observers  in  South  Africa,  recount  instances 
where  empty  entrenchments  were  fired  upon  for  hours  after 
the  guns  had  been  shifted  a short  distance. 


POSITION  AND  THE  MASK 


261 


There  are  occasions,  especially  in  a bare,  rocky  country, 
with  shallow  soil,  where  cover  is  scarce  and  “digging  in”  im- 
practicable, when  it  is  wise  for  the  firing  battery  to  be 
well  provided  with  empty  bags.  A large  number  of  gunny- 
sacks  may  be  carried  on  the  carriages  and  off  horses,  which, 
when  filled  with  loose  earth  or  sand,  will  afford  much  protec- 
tion to  the  pieces  in  action  and  the  gun  details.  This  means 
of  protection  will  be  particularly  valuable  against  shrapnel 
and  infantry  fire,  as  all  spaces  in  and  about  the  shields  of  the 
guns  may  be  quickly  filled  in  with  the  sand  bags.  A number  of 
bags  could  even  be  filled  before  the  guns  take  up  an  exposed 
position,  and  be  taken  forward  on  the  limbers. 

Creeping. — It  will  frequently  occur  in  action  that  the  act 
of  driving  the  guns  into  actual  position  will  greatly  expose 
the  teams,  by  reason  of  the  fact  that  the  animals  necessarily 
precede  the  pieces  and  will  remain  in  view  of  the  enemy, 
perhaps  on  the  sky  line,  when  the  rear  crest  position  is  quite 
near  the  actual  crest.  In  such  case,  not  only  will  the  teams 
loom  up  against  the  sky,  offering  an  excellent  target  to  hostile 
fire,  but  even  if  no  loss  of  animals  is  sustained  the  position  of 
the  guns  will  be  unwisely  advertised  among  the  watchful 
enemy,  the  principal  advantage  of  the  rear  crest  position 
thereby  being  sacrificed.  To  avoid  this  result  it  will  frequently 
be  best  to  unlimber  in  rear  of  the  actual  position  to  be  taken 
up  and  post  the  pieces  by  hand,  this  in  spite  of  the  enormous 
labor  and  delay  entailed  by  the  accidents  of  the  ground  which 
will  often  be  most  adverse.  This  method  is  known  as  “creep- 
ing,” and  has  elicited  a volume  of  discussion  abroad,  pro  and 
con,  entirely  incommensurate  with  its  technical  importance. 
The  American  soldier,  characterized  by  ready  expediency, 
views  such  a matter  as  more  in  the  nature  of  an  obvious  make- 
shift than  as  one  involving  a mooted  tactical  principle.  Tech- 
nical treatises  containing  elaborate  discussions  of  such  things 
do  much  to  impair  the  sympathy  of  an  earnest  seeker  for  pro- 
fessional information.  The  writer  personally  witnessed  the 


262 


GUNNERY 


creeping  method  adopted  upon  the  initiative  of  a chief  of 
section  at  the  memorable  Leon  Springs  (Texas)  maneuvers, 
and  ventures  the  assertion  that  this  particular  gunner  was  not 
a student  of  tactics. 

Visibility. — In  taking  up  positions  for  direct  fire  the  ques- 
tion of  visibility  is  all-important.  Every  precaution  possible 
should  be  taken  to  obscure  the  movements  of  the  guns  and 
their  positions. 

The  keynote  of  a landscape  is  confusion  of  detail.  All 
natural  objects  are  irregular  in  shape  and  complex  in  outline. 
Any  symmetrical  object,  such  as  a gun-carriage,  tends  to 
catch  the  eye  at  once.  In  nature  there  are  no  straight  lines 
(except  the  surface  of  water),  no  circles,  and  no  squares. 

Again,  there  are  no  sharp  contrasts  in  nature;  the  color  and 
tone  of  all  natural  objects  are  infinitely  varied.  For  this 
reason,  any  object  of  uniform  color,  such  as  the  side  of  a house  or 
the  flat  surface  of  a gun-shield,  attracts  attention  immediately. 

Lastly,  natural  objects  do  not  move.  So  long  as  a man  or 
a horse  keeps  still  he  escapes  notice.  The  hunter  who  sits 
forLours  waiting  for  a shot  knows  this  well;  he  also  knows  that 
the  erect  figure  of  a man  is  unlike  anything  in  nature,  and  care- 
fully avoids  the  upright  position.  The  stealthy  Indian 
crouches  as  he  creeps  up  to  his  quarry.  It  was  a standing  order 
in  Natal  that  when  men  were  seen  erect  on  the  sky  line  the 
troops  were  on  no  account  to  fire  on  them,  as  they  could  not 
possibly  be  Boers.  At  first  erect  dummies  were  placed  along 
the  route  of  the  British  troops,  who  invariably  fired  upon  them, 
thus  disclosing  their  own  position  to  nearby  sharpshooters, 
who  worried  and  harassed  the  bravest  men  into  a state  of 
demoralization.  Few  men  can  unflinchingly  face  death  at  the 
hands  of  an  unseen  enemy.  And  so  it  was  with  the  red-coated 
veterans  of  Braddock  who  melted  away  before  an  enemy  whose 
tactics  were  not  according  to  the  rules  of  war. 

The  most  conspicuous  feature  of  a landscape  is  invariably 
the  sky  line.  Not  only  does  any  movement  or  any  artificial- 


POSITION  AND  THE  MASK 


263 


looking  object  thereon  catch  the  eye  at  once,  but  the  sky  line 
forms  the  natural  point  of  aim  for  all  infantry.  Accordingly, 
it  is  especially  important  for  guns  to  avoid  it,  since  artillery 
in  action  is  more  stationary  than  infantry  or  cavalry,  and  has 
to  remain  longer  under  fire  before  it  can  limber  up  and  move. 

Not  only  symmetry  of  form  but  symmetry  of  order  or 
arrangement  makes  for  visibility.  A single  gun  might  escape 
notice,  but  four  guns  at  regular  intervals,  though  individually 
barely  visible,  form  a group  unlike  anything  in  nature,  and 
arouse  suspicion  accordingly. 

It  takes  a certain  period  of  time  for  a visible  but  inconspic- 
uous object  to  catch  the  eye  of  observers.  It  is  therefore 
sound  pohcy  to  reduce  the  period  of  exposure  to  a minimum, 
even  at  the  expense  of  additional  momentary  visibihty.  Thus, 
if  it  be  necessary  to  cross  a ridge  in  view  of  the  enemy,  the 
best  way  is  to  form  line  under  cover  and  let  every  carriage 
cross  as  nearly  as  possible  simultaneously.  If  the  opposite 
plan  be  adopted,  and  it  be  attempted  to  steal  over  in  column 
of  route,  then  the  first  carriages  may  possibly  get  over  before 
the  enemy  reahzes  what  is  happening,  but  those  following  are 
likely  to  suffer  severely. 

In  pushing  forward  guns  in  close  support  of  infantry,  it 
would  be  foolish  to  trot  a section  across  the  open  within  1,500 
yards  of  a position,  with  every  gun  and  rifie  of  the  defenders 
ready  to  open  upon  it.  But  when  the  defenders  are  thoroughly 
engaged  in  repelfing  an  assault,  their  attention  will  be  fully 
concentrated  upon  the  attacking  force  nearest  at  hand.  It 
takes  time  to  perceive  a more  distant  object,  and  more  time 
to  get  the  excited  defenders  to  shift  their  fire  to  a quarter  from 
which  the  danger  seems  less  imminent.  Therefore,  a section 
exposed  for  several  minutes  only  will  have  an  excellent  chance 
of  getting  through  unscathed.  But  even  if  it  do  not,  if  the 
fire  of  the  defenders  is  drawn  to  such  an  extent  that  the  assault- 
ing columns  of  infantry  can  reach  the  position,  the  artillery 
has  fully  served  its  purpose  and  has  no  cause  to  regret  the 


284 


GUNNERY 


loss  it  may  have  sustained,  unless  the  casualties  could  have 
been  avoided  and  the  same  results  accomplished. 

We  will  now  consider  the  application  of  the  foregoing  prin- 
ciples to  service  conditions. 

The  service  uniform  of  the  troops  has  been  rendered  as 
inconspicuous  as  possible.  Most  of  the  flashing  metal  work 
which  we  used  to  display  has  disappeared,  and  even  the  har- 
ness now  used  is  of  inconspicuous  design  and  color.  While 
the  color  of  our  material  is  perhaps  the  best,  yet  there  is  an 
undesirable  uniformity  for  service  conditions,  though  this  is 
desirable  in  time  of  peace.  In  actual  service  the  smartness 
in  appearance  of  the  guns  and  carriages  should  be  sacrificed 
to  invisibility,  and  they  will  probably  be  mottled,  clouded, 
or  chequered.  The  undersides  of  the  carriages  are  in  shadow; 
these  parts  are  very  dark,  forming  the  most  visible  features  of 
the  equipment.  This  can  be  compensated  for  by  giving  the 
under  surfaces  a lighter  tint. 

Wild  animals  are  usually  of  the  color  of  their  native  cover. 
This  is  also  true  of  birds,  such  as  the  quail,  and  of  reptiles. 
Not  only  are  animals  tinted  to  suit  their  surroundings  but  they 
are  shaded  to  compensate  for  shadows.  Many  of  them  will  be 
found  lighter  along  the  breast  and  belly  than  on  the  back, 
making  their  outline  practically  indistinguishable  at  a short 
distance. 

The  flat  front  of  a gun-shield  forms  a reflecting  surface  which 
no  amount  of  paint  can  hide.  It  will  be  found  advisable  at 
times,  in  the  absence  of  suitable  brush,  to  break  the  surface 
by  hanging  gunbuckets,  sacks,  blankets,  coiled  prolonges,  and 
miscellaneous  stores  upon  it.  Here  it  may  be  said  that  “ bush- 
ing up”  a gun  by  sticking  brush  in  the  wheels  and  hanging 
it  upon  the  shield  is  difficult  to  do  artistically  and  usually 
makes  it  more  conspicuous  than  before.  Otherwise  than  bj^ 
its  tendency  to  reflect,  the  gun-shield  does  not  on  the  whole 
add  to  the  visibility  of  the  gun.  We  all  know  the  distinctive 
appearance  of  a gun  on  a sky  line,  with  a wheel  sticking  up  on 


POSITION  AND  THE  MASK 


265 


each  side  and  the  muzzle  in  the  middle.  When  the  space 
between  the  top  of  the  wheels  is  filled  by  the  shield,  it  tends  to 
obscure  the  character  of  the  object,  even  if  its  conspicuousness  is 
not  reduced  very  greatly.  Moreover,  the  shield  hides  the  move- 
ment of  the  detachment,  which  movement  often  enables  the  gun 
to  be  located,  or  the  character  of  the  object  to  be  determined. 

The  placing  of  a caisson  immediately  alongside  of  a gun 
unfortunately  adds  to  the  visibility  of  the  position.  It  would 
be  much  better  from  the  standpoint  of  visibility  alone  to  post 
the  caissons  in  rear  of  a crest.  The  disadvantages  in  other 
respects,  however,  make  the  prescribed  position  the  better  of 
the  two.  Not  only  is  there  great  danger  of  its  being  struck 
in  rear,  but  the  casualties  among  the  men  supplying  the 
ammunition  while  crossing  over  the  crest  are  greater.  In  the 
parallel  position  the  entire  detachment  is  behind  the  shields 
of  the  two  carriages. 

Modern  nitro-powder  gives  very  little  smoke,  but  the  broad 
white  flash  from  the  muzzle  is  conspicuously  visible,  especially 
against  a dark  background,  which  should  accordingly  be 
avoided  when  practicable.  It  has  been  found  that  at  night- 
time the  flare  from  the  muzzle  can  be  seen  over  a crest  at  a 
great  distance  when  the  piece  is  within  20  feet  of  the  crest. 
Flash  defilade  is  therefore  greater  at  nighttime  than  by  day. 
The  only  means  of  concealing  the  flash  of  the  guns  at  direct 
fire  is  by  placing  them  behind  a screen,  such  as  a row  of  thinly 
growing  trees,  that  the  gunners  can  see  through.  It  is,  how- 
ever, the  exception  that  such  a natural  feature  is  available. 

It  has  been  proposed  to  fix  a shield  to  the  gun,  about  2 feet 
in  front  of  the  muzzle,  with  an  aperture  through  which  the 
projectile  may  pass.  The  impact  of  the  gases  on  this  shield 
would  help  check  the  recoil,  while  the  visible  flash  would  be 
materially  reduced.  The  idea,  as  yet,  has  not  assumed  prac- 
tical form. 

Both  when  moving  into  position  and  when  in  action  the 
dust  thrown  up  often  betrays  the  presence  of  the  battery. 


266 


GUNNERY 


On  the  defensive,  when  there  is  plenty  of  time  for  preparations, 
it  is  desirable  to  water  the  ground  in  front  of  the  muzzles.  In 
a dry  place,  the  rush  of  gas  and  air  upon  discharge  causes  a 
cloud  of  dust  to  rise  which,  added  to  what  httle  smoke  there  is, 
indicates  with  certainty  to  a watchful  eye  the  position  of  the 
guns,  even  though  they  be  otherwise  well  screened. 

In  moving  into  position,  artillery  should  always  avoid 
dusty  roads  when  sod  and  fields  are  at  hand.  Often,  a most 
excellent  position  will  be  disclosed  by  a dust  cloud  when  the 
use  of  a different  route,  even  though  a little  longer,  would  have 
prevented  the  “give  away.”  Not  only  will  the  dust  cloud 
inform  the  scouts  and  observers  of  the  enemy  as  to  the  exact 
direction  of  the  approaching  guns,  but  also  of  the  probable 
number  of  the  guns  and  the  distance  they  are  being  posted 
behind  the  covering  screen.  If  it  be  constantly  borne  in  mind 
that  a dust  cloud  serves  exactly  the  same  purpose  with  respect 
to  a battery  that  the  smoke-producing  matrix  of  a shrapnel 
does  with  respect  to  the  point  of  burst  of  the  projectile,  the 
artillery  officer  will  require  few  cautions  concerning  the  danger 
of  dust. 

In  addition  to  dummy  entrenchments,  screens,  etc.,  erected 
for  the  purpose  of  diverting  hostile  fire,  dust  and  smoke  may 
be  created  away  from  the  true  position  of  the  guns.  This 
was  done  very  effectively  by  the  Boers. 

Indirect  Fire. — For  a field  gun  the  angle  of  descent  of  a 
shell  is  about  one-third  greater  than  the  angle  of  elevation. 
If  a battery  be  firing  at  3,600  yards,  which  corresponds  to  about 
6 degrees  of  elevation,  then  the  angle  of  descent  of  the  pro- 
jectiles will  be  8 degrees.  If,  therefore,  two  batteries  of 
similar  guns  are  firing  at  each  other,  both  being  under  cover 
so  that  their  projectiles  barely  clear  the  covering  crests,  each 
will  be  able  to  hit  the  other.  In  other  words,  when  engaging 
a hostile  battery  it  is  impossible  to  obtain  natural  cover  from 
its  fire.  If  Battery  “A”  can  hit  Battery  “B”,  the  latter  can 
hit  the  former. 


POSITION  AND  THE  MASK 


267 


The  advantage  of  covered  positions  is  solely  due  to  con- 
cealment from  the  enemy’s  view.  It  follows,  therefore,  that 
the  cover  afforded  by  trees,  houses,  hedges,  etc.,  is  just  as  good 
as  that  afforded  by  a rise  of  ground  or  an  intervening  hillside. 
A practical  exception  to  this  rule  is  that  the  cover  must  not 
be  of  such  a nature  as  to  act  as  a penetrable  screen  to  burst 
the  enemy’s  shrapnel  within  effective  distance  of  the  battery. 

Example  of  Japanese  Methods. — Illustrative  of  the  Japan- 
ese methods  of  preparing  a position  before  opening  fire,  both 
with  a view  to  screening  the  guns  and  protecting  the  material 
and  personnel  in  the  event  they  were  located,  the  instance  of 
the  Yalu  may  be  cited. 

The  Japanese  artillery  were  given  orders  to  mass  on  Kin- 
teito  Island,  about  opposite  the  Russian  center,  during  the 
night  of  April  29th-30th.  They  were  to  open  fire  at  the  first 
good  opportunity  given  them  by  the  Russian  artillery.  If 
the  Russian  guns  gave  them  no  opening  they  were  not  to  fire 
at  all.  In  anticipation  of  a duel,  by  daybreak  on  the  30th  the 
whole  of  the  artillery  of  the  Second  Division,  together  with 
the  five  batteries  of  twelve-centimeter  howitzers,  in  all  thirty- 
six  field  guns  and  twenty  howitzers,  had  been  admirably 
entrenched  on  the  soft,  sandy  soil  of  the  island,  with  the  Yalu, 
like  a huge,  impassable  moat,  flowing  along  its  northern  face. 
Every  advantage  of  the  natural  lie  of  the  ground  was  taken, 
and  much  artifice  was  employed  to  conceal  the  position  from 
the  hostile  gunners  on  the  north  bank  of  the  river,  2,000  yards 
or  more  away.  Trees  were  transplanted  a short  distance  in 
front  of  the  batteries  to  hide  the  tell-tale  flash  of  discharge, 
and  were  carefully  chosen  from  among  those  which  were 
growing  either  directly  in  front  or  directly  behind  the  intrench- 
ment  which  was  to  be  concealed.  Thus  next  morning  the 
landscape  appeared  unchanged  from  the  Russian  side  of  the 
river,  as  the  fact  that  a tree  of  a particular  shape  had  advanced 
or  retired  200  or  300  yards  during  the  night  was  naturally 
imperceptible.  Poles  were  stuck  into  the  sand  and  connected 


268 


GUNNERY 


by  a string  on  which  branches  were  suspended.  The  earth  dug 
out  of  the  deep  gun  pits  was  most  carefully  and  with  great 
labor  scattered  broadcast,  so  as  not  to  disclose  any  irregularity 
of  terrain.  The  howitzer  pits  and  epaulments  were  connected 
by  trenches,  and  numbers  of  covered  ways  leading  down  to 
the  river  bank  were  dug  to  insure  a plentiful  supply  of  water 
for  laying  the  dust  which  is  otherwise  so  apt  to  rise  with  the 
shock  of  discharge  and  give  away  a position. 

When  all  had  been  done  that  could  be  done  to  insure 
concealment,  then  all  was  done  that  could  be  done  in  the  time 
left  to  insure  safety  if  concealment  should  chance  to  fail. 
Bomb-proof  shelters  were  made  for  the  men,  and  were  dug 
so  deep  and  so  strongly  roofed  over  with  heavy  baulks  of 
timber  and  earth  that  they  would  have  resisted  heavj"  siege 
artillery,  let  alone  the  field  guns,  which  were  all  they  had  to  fear. 

General  Sir  Ian  Hamilton  of  the  British  Army  declares 
that  he  could  not  detect  these  entrenchments  from  the  other 
side  of  the  river,  even  though  he  had  just  inspected  them  and 
knew  about  where  they  were  located.* 

Thus,  screened  from  observation  and  protected  against  fire, 
every  possible  precaution  had  been  taken  toward  mintmizmg 
the  effect  of  the  enemy’s  guns.  It  now  only  remained  to 
perfect  the  arrangements  for  offensive  action.  W"ith  this 
object  two  observation  stations  were  established  at  command- 
ing points  some  3,000  or  4,000  yards  in  rear  of  the  batteries, 
from  whence  a good  view  could  be  obtained  of  the  Russian 
camp  behind  Chiulienchang,  and  of  the  lateral  communica- 
tions, such  as  they  were,  which  ran  in  rear  of  the  Russian 
entrenchments.  These  observation  stations  were  connected 
with  the  howitzer  batteries  by  telephone,  and  both  batteries 
and  observation  stations  having  duplicate  maps  of  the  enemy’s 
position  marked  out  in  small  squares,  the  observers  on  the 
southern  heights  were  able,  by  merely  telephoning  down  the 
number  of  a square,  to  switch  the  whole  fire  effect  of  the 
*A  Staff  OflBcer’s  Scrap-Book,  Vol.  1,  p.  111. 


POSITION  AND  THE  MASK 


269 


masked  batteries  on  to  any  spot  where  they,  from  their  posts 
of  vantage,  could  see  a suitable  target  present  itself.  Plat- 
forms were  also  erected  in  trees  on  the  flanks  of  the  batteries, 
from  whence  officers  could  make  local  observations  of  the 
effect  of  their  fire. 

When  we  consider  that  all  of  this  was  accomplished  in  one 
night,  unknown  to  a watchful  enemy,  and  that  so  far  the 
First  Army  had  to  fight  its  first  engagement,  all  the  more 
remarkable  does  it  seem.  The  Battle  of  the  Yalu  was  the 
opening  scene  of  the  Manchurian  tragedy.  How  had  the 
Japanese  acquired  such  a mastery  of  practical  gunnery?  Not 
by  experience,  for  modern  field  guns  were  as  new  to  them  as  to 
the  Russians  who  posted  theirs  so  poorly;  a comparison  of  the 
positions  of  the  artillery  of  the  two  armies  at  the  Yalu  is  as 
those  of  professional  and  amateur.  The  Japanese  were  invis- 
ible and  comparatively  invulnerable;  the  Russians  were  con- 
spicuous and  everywhere  most  vulnerable.  The  latter  never 
had  a chance.  The  overwhelming  superiority  of  their  72 
guns  and  20  howitzers,  not  only  in  weight  of  metal  but  in 
position,  was  quickly  overcome,  and  thus  the  Japanese  were 
enabled  to  crush  their  opponents.  In  thirty  minutes  the 
Russian  guns  were  silenced. 

“Why,  why  did  the  Russian  great  general  staff  disdain  to 
take  a lesson  from  the  Boers,  who  had  so  recently  repeated 
for  the  benefit  of  the  British,  and  for  that  of  all  the  world  as 
well,  if  it  chose  to  take  heed,  the  lesson  of  how  an  inferior 
artillery  should  be  worked?”  says  General  Hamilton. 

The  fact  remains,  however,  that  as  the  war  progressed  the 
two  artilleries  drew  away  from  the  mask,  sacrificing  the  effect 
of  their  fire  to  safety  of  position. 

Clearing  the  Mask. — When  position  for  indirect  fire  is 
to  be  occupied  it  is  necessary  to  make  sure  that  the  pro- 
jectiles from  each  gun  will  clear  the  mask.  But  this  is  not 
all  that  is  necessary,  for  if  it  were  necessary  to  give  the  guns 
such  an  elevation  for  this  purpose  that  the  projectiles  would 


270 


GUNNERY 


pass  over  and  beyond  the  target  the  fire  would  be  useless. 
The  effect  of  the  elevation  on  the  range  must  always,  there- 
fore, be  kept  in  mind. 

If  the  mask  is  near  at  hand  and  the  guns  are  in  position, 
by  sighting  through  the  bores  it  may  be  ascertained  whether 
the  projectile  will  clear;  but,  as  a rule,  the  position  must  be 
selected  before  the  guns  are  placed,  hence  sighting  through  the 


bores  is  impossible.  Again,  if  the  mask  is  distant,  while  the 
axis  of  the  piece  might  clear,  the  trajectory  for  the  range  might 
not  pass  over  the  mask. 

In  Figure  2 the  trajectory  for  T at  range  GT  clears,  but  the 
trajectory  for  T at  range  GTi  will  not.  For  both  ranges  the 
line  of  fire,  which  is  the  axis  of  the  piece  prolonged,  clears  the 
mask. 

Again,  even  if  it  should  be  found  that  the  trajectory  for  a 
given  range  would  clear  the  mask,  the  correction  for  angle  of 
site,  if  one  of  depression,  might  cause  the  projectile  to  strike 
the  mask,  for,  as  we  have  seen,  an  angle  of  site  for  depression 
is  in  effect  a shortening  of  the  range  of  the  trajectory  wdth 
respect  to  the  horizontal.  The  foregoing  is  illustrated  in 
Figure  3,  where  the  range  is  the  same  but  the  angles  of  site  for 
T,  Ti,  and  T2  are  different. 

Now  it  is  plain  that  if  we  can  find  the  distance  of  the  mask 
from  the  guns  and  its  height,  and  can  then  determine  the 
height  of  the  trajectory  at  that  point,  we  can  tell  whether  the 
trajectory  will  clear. 

If  the  crest  of  the  mask  is  very  distant,  the  distance  thereto 
can  be  determined  in  the  same  manner  as  the  distance  to  the 
aiming  point,  that  is  by  the  telescope  and  a measm’ed  base. 


POSITION  AND  THE  MASK 


271 


by  the  range  finder,  and  by  estimation.  In  the  last  case,  it 
would,  of  course,  be  impractical  to  verify  the  distance  by  fire, 
when  in  action. 

The  height  of  the  mask  in  mils  can  be  determined  by  use 
of  the  B.  C.  ruler  or  more  accurately  by  the  B.  C.  telescope. 
Knowing  the  distance  of  the  crest  and  its  height  in  mils,  the 
height  in  feet  can  easily  be  determined.  Thus,  if  the  crest  is 
1,000  yds.  distant  and  20  mils  high,  it  is  60  feet  high,  since  each 
mil  at  1,000  yds.  is  1 yd.  or  three  feet. 

We  must  now  determine  how  high  in  feet  the  trajectory  is 


at  a point  1,000  yds.  from  the  guns.  The  height  of  the  traject- 
ory above  the  horizontal  at  any  point  depends,  of  course,  upon 
the  range  and  the  angle  of  site,  as  we  have  seen  in  Figme  2. 
This  height  may  be  found  by  the  use  of  the  Battery  Command- 
er’s Ruler.  This  instrument  is  fully  described  and  its  general 
use  explained  on  pp.  114-116  of  the  Handbook  for  Three-Inch 
Material.  It  contains  a white  metal  rule,  which  slides  in  a 
groove  in  a brass  rule.  The  slide  rule  is  graduated  in  mils  from 
— 24  through  0 to  + 284.  The  scale  of  the  brass  rule  gives 
hundreds  of  yards  of  range.  If  the  angle  of  site  is  30  mils,  the 
number  30  on  the  slide  rule  is  set  opposite  the  division  on  the 
range  scale  indicating  the  distance  to  the  crest  of  the  mask. 

The  reading  on  the  slide  opposite  the  division  on  the  brass 
rule,  corresponding  to  the  range  of  the  target,  gives  the  height 
in  mils  of  the  trajectory  at  the  crest  of  the  mask.  In  other 
words,  the  brass  scale  is  for  ranges  in  yards  and  the  white 
slide  gives  heights  in  mils.  Place  the  angle  of  site  opposite 


272 


GUNNERY 


the  range  to  the  mask.  The  angle  opposite  the  range  of  the 
target  gives  height  of  the  trajectory  at  the  mask. 

Suppose  we  find  by  this  method  that  the  trajectory  is  30 
mils  high  at  the  mask.  If  the  mask  is  1,000  yds.  distant  the 


trajectory  is  30  yds.  or  90  feet  high  at  that  point.  Now  if 
the  mask  is  60  feet  high  the  projectile  will  clear  by  30  feet. 
But  if  the  height  of  the  trajectory  is  found  to  be  15  mils  or  45 
feet,  and  the  mask  is  60  feet  high,  the  projectile  will  strike  15 
feet  below  the  crest.  Hence,  a longer  range  must  be  used,  or  a 
greater  angle  of  site,  or  a combination  of  the  two.  It  is  not 
necessary,  however,  to  add  to  the  range  in  the  direction  of  the 
target.  The  increase  can  be  secured  by  moving  the  pieces 
away  from  the  target  or  back  from  the  mask,  unless  in  so  doing 


the  guns  would  be  moved  up  to  an  elevation  at  which  they 
could  be  seen  by  the  enemy,  thus  losing  the  cover  of  the  mask. 

When  the  guns  are  at  Gi  (Figure  4),  the  trajectory  does  not 
clear,  but  upon  being  moved  back  to  G (an  increase  of  range), 
the  increase  in  the  height  of  the  trajectory  is  sufficient  to  cause 
it  to  clear  the  mask.  But  suppose  (Figure  5)  the  guns  in 
being  moved  backward  were  moved  down  grade. 

The  tendency  in  such  a case  is  to  draw  down  the  trajectory, 
which  would  have  been  GiT  had  the  guns  been  moved  back- 
ward at  the  same  level  as  G.  When  the  guns  were  at  G the 
angle  of  site  was  normal,  and  so  it  would  have  been  at  Gi. 


POSITION  AND  THE  MASK 


273 


But  at  Gi  it  is  300+  or  it  has  increased.  Hence,  as  the  angle 
of  site  changes  when  the  guns  are  lowered,  we  must  be  careful 
that  the  increase  in  the  height  of  the  trajectory,  gained  by 
lengthening  the  range,  is  not  counteracted  by  the  effect  of 
lowering  the  position  and  changing  the  angle  of  site. 

It  will  be  seen  (Figure  6)  that  as  the  guns  are  moved  to 
higher  positions  the  angle  of  site  changes  from  300  to  300  — 
and  that,  as  it  is  changed  by  elevating  the  positions  of  the 
pieces,  the  tendency  is  to  raise  the  trajectory  above  the  mask, 
as  GiT  and  G"T. 

If  the  angle  of  site  remained  constant,  that  is  if  T moved 


downward  as  fast  as  the  positions  of  the  guns  were  elevated, 
only  an  increase  of  range  would  raise  the  trajectory  over  the 
mask.  From  the  foregoing  the  following  rules  may  be  deduced : 

1.  By  moving  the  guns  backward  from  the  mask  the  tra- 
jectory is  heightened; 

2.  By  moving  the  guns  backward  and  downward  we  coun- 
teract, in  a measure,  this  increase  in  elevation. 

3.  By  moving  the  guns  backward  and  upward  we  add  to 
this  increase  in  elevation. 

From  the  following  table  we  can  plot  the  curve  of  a tra- 
jectory with  serviceable  accuracy.  The  maximum  ordinate, 
as  we  know,  is  the  perpendicular  to  the  highest  point  or  summit 
of  the  curve.  From  the  B.  C.  ruler  the  exact  height  of  the 
trajectory  in  mils  at  every  point  for  any  range  can  be  ascer- 
tained by  placing  the  normal  angle  of  site  300  opposite  the 
point  the  elevation  of  which  is  desired,  and  reading  the  angle 
opposite  the  range  of  the  target. 


274 


GUNNERY 


A vivid  impression  of  the  rapid  increase  in  the  height  of 
the  trajectory  for  increased  ranges  is  obtained  when  we  plot 
these  curves  to  scale.  This  interesting  problem  should  be 
solved  by  every  student  of  gunnery.  For  instance,  for  a 
range  of  500  yds.  the  projectile  rises  to  a point  4.3  feet  above 
the  line  from  gun  to  target,  the  elevation  increasing  to  17.3 
feet  for  1,000  yds.,  975.0  feet  for  5,000  yds.,  and  1,992.0  for 
6,500  yds.  The  highest  possible  mask  which  can  be  used  at  a 
range  of  1,000  yds.  is  17.3  ft.,  situated  a little  nearer  the  tar- 
get than  to  the  gun  because  the  maximum  ordinate  is  not  at 
the  middle  of  the  range.  This  is  easily  understood  when  we 
plot  the  curve  and  compare  the  angle  of  fall  with  the  angle  of 
departure.  The  former  wiU  be  invariably  found  the  greater 
of  the  two. 

At  a range  of  2,000  yds.  it  is  possible  to  fire  over  a mask 
93.1  ft.  high;  and  at  a range  of  4 miles  one  could  fire  over  a 
mountain  over  2,000  feet  high,  situated  about  2 miles  dis- 
tant. 

The  height  of  a possible  mask  diminishes  rapidly  with  its 
proximity  to  the  target  as  well  as  to  the  guns. 


Range  (Yards) 

Angle  of 
Departure 

Angle  of  Fall 

Maximum  Ordinate 
(Feet) 

500 

0°  31.9' 

0°  35.3' 

4.3 

1,000 

1°  11.2' 

1°  27.3' 

17.3 

1,500 

1°  59.4' 

2°  38.6' 

45.3 

2,000 

2°  56.7' 

4°  07.6' 

93.1 

2,500 

4°  01.8' 

5°  48.8' 

163.5 

3,000 

5°  12.0' 

7°  41.2' 

257.0 

3,500 

6°  28.7' 

9°  43.7' 

378.0 

4,000 

7°  54.2' 

12°  02.9' 

536.0 

4,500 

9°  28  5' 

14°  37.3' 

731.0 

5,000 

11°  10  1' 

17°  26.0' 

975.0 

5,500 

13°  10.1' 

20°  29.0' 

1,263.0 

6,000 

15°  10.8' 

23°  40.0' 

1,598.0 

6,500 

17°  12.6' 

27°  06.8' 

1,992.0 

POSITION  AND  THE  MASK 


275 


In  calculating  clearance  a good  margin  should  always  be 
allowed  for  the  four  guns  of  a battery  are  seldom  at  exactly 
the  same  level,  and  the  same  holds  true  of  the  batteries  of  a 
battalion  and  so  on.  Especially  important  is  this  margin  of 
clearance  when  the  infantry  is  advancing  over  the  intervening 
slopes  and  when  the  crest  of  the  mask  is  near  the  guns.  In  the 
first  case,  much  damage  may  be  caused  by  bursts  on  graze 
among  our  own  troops.  In  the  second  case,  the  explosion  of 
shrapnel,  and  particularly  of  shell,  in  the  immediate  front  of 
the  battery  is  highly  demorahzing,  whether  caused  by  our  own 


or  hostile  guns.  In  addition  to  the  moral  effect  many  casual- 
ties may  result,  and  the  exact  position  of  the  battery  may  be 
disclosed  to  the  eye  of  the  enemy. 

A good  rough  working  rule  for  determining  the  height  of 
the  trajectory  may  be  deduced  from  our  knowledge  of  its 
curve.  Every  trajectory,  as  we  have  seen  in  Ballistics,  approxi- 
mates an  analytical  curve,  and  that  curve  may  be  analyzed 
with  respect  to  the  horizontal  and  the  vertical  ordinates  and 
the  value  of  each  coordinate  expressed  algebraically.  In  other 
words  (Figiue  7)  the  vertical  ordinate  y of  the  point  M bears  a 
definite  relation  to  its  horizontal  ordinate  x,  the  relative 
values  of  the  ordinates  depending  upon  the  velocity  of  the 
projectile  and  the  resistance  of  the  atmosphere. 


276 


GUNNERY 


Percin’s  Rule. — For  cases  in  which  the  height  of  the  mask 
in  yards  is  known  Gen.  Percin,  of  the  French  artillery,  has 
deduced  a simple  rule  of  approximation.  For  the  actual  tra- 
jectory he  has  substituted  a parabola  passing  through  the 
origin  and  the  point  of  fall,  whose  ordinates  at  all  points  of  the 
range  are  inferior  to  the  ordinates  of  the  real  trajectory.  The 
equation  of  the  Percin  parabola  is 


4y  = x(R— x), 

in  which 

y is  the  ordinate  in  yards  corresponding  to  any  point  z. 

X is  in  the  general  sense  any  abscissa;  in  the  special 
sense  it  is  the  distance  from  gun  to  mask  in  hundreds 
of  yards. 

R is  the  entire  range  from  gun  to  object  in  hundreds 
of  yards. 

Solving  for  x, 

X=  -Nu 

(R-x), 

from  which  it  is  seen  that,  under  the  rule,  a projectile  will  clear 
the  mask  when  fired  at  a distance  from  the  mask  equal  to  four 
times  the  height  of  the  mask  in  yards,  divided  by  the  range 
from  mask  to  object  in  hundreds  of  yards. 

Example:  The  range  from  mask  to  target  is  4,000  yards; 
height  of  mask  20  yards. 

4y  = 80, 

(R  — x)  =40, 

x = 200  yards. 

At  200  yards  the  angle  of  site  of  the  mask  is  100  mils;  the 
angle  of  departure  corresponding  to  range  of  4,200  yards  is 
151.4  mils;  hence  it  will  be  seen  that  the  rule  gives  a large 
factor  of  safety  for  horizontal  ranges.  Even  for  an  angle  of 


POSITION  AND  THE  MASK 


277 


site  of  target  as  low  as  250  the  projectiles  in  this  case  would 
clear  the  mask. 

Let  S = angle  of  site  of  mask; 

y 

then  S = :^=10-' 

10  X 

y_ 

X 10 

From  the  equation  of  the  parabola  above 

^ = i (R— x), 

X 

or 

^=i  (R-x), 
or 

S = 2.5  (R— x). 


From  which  it  is  seen  that  the  trajectory  will  clear  if  the  guns 
are  placed  at  a distance  from  the  mask  such  that  the  angle  of 
site  of  the  mask  from  the  gun,  in  mils,  is  equal  to  or  less  than 
two  and  one-half  times  the  distance  from  mask  to  target  in 
hundreds  of  yards. 

Miles’  Method. — It  is  not  always  practicable  to  employ 
the  B.  C.  ruler  or  Percin’s  rule  in  solving  the  problem  of  clear- 
ing the  mask.  Lieut.  Miles  of  the  United  States  Army  offers 
an  interesting  solution. 

Suppose  for  instance  the  mask  is  a gently  sloping  crest 
within  100  yards  of  the  guns.  To  use  the  sliding  scale  we 
must  know  the  distance  from  the  guns  to  the  top  of  this  crest. 
It  is  often  difficult  to  locate  this  exact  point;  but  even  if  we  do 
locate  it,  and  apply  the  sliding  scale  method,  nothing  more  is 
deternr  ined  than  that  the  guns  will  or  will  not  clear  that  par- 
ticular point.  If  they  do  clear  it  there  may  be  another  slightly 
lower  point  nearer  the  guns  which  may  touch  or  be  above  the 


278 


GUNNERY 


curve  of  trajectory.  To  the  solution  of  the  problem  in  this 
case,  then,  the  sliding  scale  method  is  not  in  practice  applicable. 

The  following  method  is  particularly  applicable  to  this 
common  case  of  the  guns  being  on  the  reverse  slope  of  a shghtly 
convex  hill.  The  two  factors  considered  are — 

(a)  The  angle  of  departure  of  the  projectile. 

(b)  The  angular  height  of  the  mask  above  the  guns. 

In  order  that  the  projectile  may  clear  the  mask  (a)  must  be 
greater  than  (b). 

If,  as  in  the  first  form  of  the  problem,  we  wish  to  find  the 
minimum  range,  (b)  is  first  measured.  The  value  of  (a)  is  then 
established,  since  it  must  be  slightly  greater  than  (b).  And, 
since  (a)  is  equal  to  the  algebraic  sum  of  the  angle  of  site  and 
the  elevation  of  the  gun  due  to  range,  the  elevation  due  to 
range  is  determined  for  any  given  angle  of  site.  By  reference 
to  a table  showing  the  elevations  for  all  ranges  the  minimiiTn 
range  is  obtained. 

If,  as  in  the  second  form  of  the  problem,  the  target  is  known, 
and  we  wish  to  find  a position  from  which  the  mask  can  be 
cleared,  one  or  more  positions  are  tried.  The  practicability 
of  clearing  from  any  trial  position  is  determined  by  measuring 
(b)  and  finding  (a)  by  adding  the  angle  of  site  of  the  target 
and  the  elevation  corresponding  to  the  range  to  the  target. 
This  elevation  is  taken  from  the  table  spoken  of  above.  The 
angles  (a)  and  (b)  having  been  determined,  the  guns  will  clear 
the  mask  from  that  trial  position  if  (a)  is  greater  than  (b), 
otherwise  not. 

Now,  as  to  the  method  of  measuring  these  various  angles, 
and  the  form  in  which  they  should  appear.  It  is  easy  to  con- 
struct a table  showing  for  all  ranges  the  angle  in  mils  of  ele- 
vation of  the  gun  due  to  range  (with  normal  angle  of  site). 
The  value  of  an  angle  in  mils,  divided  by  1000,  is  approximately 
the  tangent  of  the  angle.  This  approximation  is  sufficiently 
close,  especially  for  the  smaller  angles.  For  example,  the  tan- 


POSITION  AND  THE  MASK 


279 


gent  of  an  angle  of  200  mils  (11  degrees,  15  minutes)  is  199/1000. 
No  greater  error  is  made  if  we  take  200/1000.  The  angle  of 
site  could  similarly  be  easily  put  in  tangent  form  by  dividing 
the  mils  by  1000.  The  angle  (b),  being  an  angle  of  slope,  could 
easily  be  measured  in  tangent  form,  as,  for  example,  a slope  of 
1 on  20  from  the  guns  to  the  top  of  the  mask.  Thus  the  three 
angles  involved  are  readily  put  in  the  form  of  tangents,  with 
a common  denominator  of  1000.  If  the  reconnaissance  ofhcer 
carried  a clinometer  graduated  in  mils  the  problem  would  be 
simplified,  and  he  would,  moreover,  be  able  to  read  angles  of 
site  far  more  readily  and  accurately  than  by  any  instrument  at 
present  issued. 

How  would  this  method  of  determining  the  practicability 
of  a mask  work  out  in  the  field?  Let  us  imagine  the  typical 
case  of  an  officer  sent  out  to  find  a defiladed  position  to  fire  on  a 
given  target.  He  finds  several  positions,  each  more  or  less 
fulfilling  the  requirements  of  defilade,  good  range,  accessibility, 
etc.  He  decides  to  examine  them  in  detail,  beginning  with 
the  one  that  seems  the  most  promising.  This  position  offers 
a flash  defilade  on  the  reverse  slope  of  a slightly  convex  crest. 
He  wishes  to  determine  whether  or  not  the  guns  can  clear  the 
crest.  He  carries  a clinometer  graduated  in  mils,  and,  on 
the  case  of  the  clinometer,  a table  showing  the  elevations  in 
mils  due  to  range.  He  first  goes  to  the  top  of  the  crest  and 
there  verifies  his  first  estimate  of  the  range  (he  would  have  to  do 
this  in  any  case).  Looking  at  his  table  he  finds  the  angle  130 
mils  opposite  his  determined  range  of  4000  yards.  With  his 
clinometer  he  measures  the  angle  of  site  to  the  target — minus 
5 nuls.  He  corrects  this  for  the  position  of  the  guns  4 yards 
below  and  about  30  yards  to  the  rear — say  minus  4 mils. 
Going  to  the  proposed  position  of  the  guns  he  holds  his  clino- 
meter at  the  height  of  a gun  above  the  ground  and  measures 
the  angle  to  the  top  of  the  crest — 120  mils.  Then — 

130/1000  — 4/1000  = 126/1000,  and  is  greater  than 
120/1000.  He  sees  that  the  guns  would  just  clear  the  crest — 


280 


GUNNERY 


for  safety  they  had  better  be  moved  a little  nearer.  He  also 
is  able  to  give  the  battery  or  battalion  commander  the  correct 
range  and  angle  of  site. 

It  will  be  observed  that  unless  the  angle  of  site  of  the  target 
is  greatly  above  or  below  the  normal  the  officer  will  make  no 
appreciable  mistake  if  he  does  not  stop  to  correct  the  angle  of 
site  measured  from  the  top  of  the  crest. 

Dead  Space. — It  must  not  be  thought  that  the  sole  con- 
sideration in  taking  up  a covered  position  is  whether  or  not 
the  projectile  will  clear  the  mask.  The  flat  trajectory  of  a 
modern  field  gun  imposes  certain  limitations  on  it,  which  must 
be  borne  in  mind  when  selecting  a covered  position.  The 
angle  of  elevation  of  the  3"  gun  is  only  about  3°  for  2,000  yards 
and  5°  for  3,000  yards.  Therefore,  if  the  covered  position  be 
such  as  to  require  3 degrees  of  elevation  to  clear  the  mask,  the 
whole  of  the  foreground  within  2,000  yards  of  the  guns  will  be 
dead  space.  On  the  defensive,  then,  the  minimum  of  cover 
necessary  to,  screen  the  guns  from  hostile  view  vdll  have  to 
suffice,  since  the  guns  exist  to  repel  the  enemy  and  not  pri- 
marily to  be  hidden  by  cover. 

The  sector  of  Are  assigned  the  guns,  and  the  character 
of  the  included  terrain,  will  generally  determine  whether  a 
position  on  the  rear  crest  of  the  mask  or  one  well  back  there- 
from will  be  taken  up.  If  the  position  of  the  enemy  is  near 
the  forward  face  of  the  mask  the  position  of  the  attacking 
guns  will  necessarily  be  well  away  from  the  mask.  But  if  the 
position  to  be  attacked  is  well  in  advance  of  the  mask  it  can 
be  reached  by  the  fire  of  guns  either  just  in  rear  of  the  mask  or 
well  back  therefrom.  The  former  is  generally  the  better  posi- 
tion since  the  range  is  shorter,  the  fire  therefore  more  effective, 
and  since  the  guns  can  be  run  up  to  the  “rear  crest”  position 
if  direct  fire  becomes  necessary.  Again,  all  short  shots  are 
ineffective  as  well  as  the  “overs,”  whereas  if  the  second  posi- 
tion is  taken  the  “shorts”  may  have  a demoralizing  effect  since 
the  majority  of  them  will  be  visible. 


POSITION  AND  THE  MASK 


281 


The  principal  disadvantage  of  the  more  advanced  position 
is  that  the  enemy  will  be  more  apt  to  search  the  reverse  slope 
of  a likely  mask  than^be  terrain  well  back  therefrom  of  which 
they  can  see  no  part,  and  without  making  a reconnaissance 
know  nothing  of,  unless  a detailed  map  of  the  country  is  at 
hand. 

Danger  Angle. — When  the  rear  position  is  taken  the  crest 
of  the  mask  must  be  kept  clear  for  a distance  equal  to  the 


Fig.  8. 

front  of  the  battery,  plus  a distance  on  either  side  equal  to 
that  of  the  battery  from  the  crest.  This  is  necessary  in  order 
not  to  infringe  on  the  “danger”  angle  of  45°  from  the  muzzles 
of  the  flank  guns  with  the  true  direction  of  fire;  that  is,  if 
the  battery  is  100  yards  in  rear  of  the  crest,  it  will  require  the 
crest  to  be  kept  clear  of  other  troops  and  other  guns  for  300 
yards;  if  200  yards  in  rear,  500  yards  of  crest  must  be  unoccu- 
pied by  friendly  troops.  Hence,  the  battery  commander 
cannot  use  the  logical  position  from  which  to  make  his  obser- 
vations without  moving  far  to  the  flank;  the  best  station  being, 
of  course,  on  the  nearest  crest  from  which  the  enemy  is  visible 
beyond  the  mask. 


282 


GUNNERY 


The  entire  danger  angle  is  90°  or  1,600  mils  of  crest.  It  is 
found  in  practice  that  wild  shots  will  frequently  burst  in  this 
sector.  The  width  of  the  sector  is  determined  by  errors  in 
laying,  and  its  depth  by  premature  bursts  due  to  error  of 
fuze.  In  other  words,  a man  standing  anywhere  in  the  angle 
AGB  (Figure  8)  is  apt  to  be  killed  by  the  fire  from  his  own 
guns  at  G,  although  the  target  is  at  T. 


INDEX 


PAGE 

Absolute  Deviation  of  Fire  . . . 153 

Actual  Crest 256 

Addition,  Algebraic 52 

Adiabatic  Expansion  109 

Adjusting  Fire,  Discussion  of  . . 157 
Adjusting  Height  of  Burst  . . .231 

Adjusting  the  Range  210 

Adjustment  of  Fire  and  Percus- 
sion Fire 153,  154 

Aiming  Points,  Auxiliary,  use  of  189 


Aiming  Points,  Calculation  of  De- 
flection when  not  available 

184,  185,  186 
Aiming  Points,  Designation  of  . 164 
Aiming  Points,  Discussion  of  . . 172 
Aiming  Point,  Use  of  B.  C.  Tele- 
scope   186,  190 

Aiming  Point,  Use  of  Directed 

Piece  as 186 

Alexander,  Gen.  E.  P.,  C.  S.  A.,  XXIII 
Alexander  the  Great,  XXIII 

100,  101 

Algebraic  Expressions 50 

Alignment  of  Guns 258 

American  Civil  War XXVI 

American  Revolution  . . . XXV 
Ammunition,  Shrapnel,  138;  H. 

E.  Shrapnel,  144;  H.  E.  Shell  . 145 
Angle,  Danger,  discussed  ....  281 

Angle  of  Departure 118 

Angle  of  Descent  or  FaU  ....  129 
Angle  of  Descent  of  Shell  and 

Shrapnel 258,  259,266 

Angle  of  Fall 118 

Angle  of  Elevation  118 

Angle  of  Fall,  relation  to  flatness 

of  trajectory 127,  128 

Angle  of  Incidence  218 

283 


! Angle  of  Obliquity,  explained  . . 201 

I Angle  of  Parallax,  explained  . . 175 

Angle  of  Position 118 

Angle  of  Reflection 218 

Angle  of  Refraction 219 

Angle  of  Site,  224,  Derivation  of. 

Formula  for  226 

Angle  of  Site,  effect  of  errors 

in 228,  229 

Angle,  striking 118 

Angles  of  Departure  and  Fall  . . 230 

Angles,  Measure  of 21 

Angles,  measurement  of  ....  193 

Angles,  Vertical 169 

Angles,  relative  value  in  mils  . . 168 

Application  of  Fire 157 

Archduke  Charles  . . . XV,  XVIII 
Archimedes,  used  powder  . . . 102 

Areas 44 

Artillery,  Derivation  of  name  of  . 99 
Artillery,  Development  of  ...  100 
Atmospheric  Resistance  and  Pres- 
sure   99 

Attack,  Infantry,  manner  of  161,246 

Austerhtz XIII 

Austro-Prussian  War  . . . . XXVI 

Auxihary  Observers 239 

Azimuth 172,  173,  174,  175 

Bacon,  not  inventor  of  gun  pow- 
der   . . 102 

BaUista,  origin  and  use  of  ...  101 

Ballistics,  classified 107 

Ballistics,  exterior 116 

BaUistics,  Interior,  scope  and 

practical  results  of 108 

Ballistics,  origin  and  meaning  of  97,  98 
Battery  Commanders’  Telescope, 
used  as  Aiming  Point  ....  190 


284 


INDEX 


Battery  Commanders’  Ruler,  ex- 
plained   198 

Bayonets,  origin  of 105 

Bibliography,  for  students  . . XXV 
Boer  Entrenchments,  dmnmy  and 

dual 260 

Bracket  of  Fire  and  Brackets  154,  155 

Bracketing  for  Range 211 

Braddock,  troops  of 262 

Brahmins,  used  powder  ....  102 
Breech-loaders,  origin  of  ....  106 
British  Troops  in  South  Africa 

and  dummies 262 

Bull  Run,  Battle  of XIX 

Bunyon XIII 

Burst,  Mean  Point  of 232 

Burst,  Normal  Height  of  . . . .231 
Burst,  Point  and  Interval  of,  with 

table  140, 141 

Bursting  of  Shrapnel,  tests  of  . . 142 
Bursts,  effect  of  error  in  Angle  of 

Site  on 234 

Bursts,  on  graze  and  in  air,  effect 

of 143,144 

Caesar XV,  XXIII,  102 

Caligula,  used  powder 102 

Capacity,  Measures  of 20 

Capacity  of  the  gun Ill 

Carter,  Col.,  C.  S.  A XXIII 

Catapult,  origin  and  use  of  ...  101 

Chamber  of  gun 112 

Charles  VIII,  Artillery  of  ...  103 

Chew,  Col.,  C.  S.  A XXIII 

Chickahominy  River XIX 

China-Japan  War XXVII 

Circle,  number  of  mils  in  ...  . 168 

Circles 39 

Classification  of  Field  Artillery  XXIX 

Clausewitz XIV 

Clearance  of  Mask,  calculating  . 275 

Clearing  the  Mask  269 

Clearing  the  Mask,  formula  for  123 

Cleon XIII 

Clive  XV 

Close  Range 209 


PAGE 


Combustibles 61 

Combustion,  Ordinary 61 

Combustion,  very  rapid  ....  63 

Common  Fractions 7 

Concealment,  discussed  ....  262 
Concealment,  Japanese  methods 

of  267 

Concentration  of  Fire,  formula 

for  179 

Cone  of  Dispersion  of  Shrapnel 

balls 139 

Congreve  Rockets,  origin  of  . . 105 
Continuous  Fire,  discussion  of  . . 158 

Convergence  of  Fire 181 

Convergence  Difference,  formula 

for  181 

Correcting  for  Obhquity,  rules 

for 204 

Correction  for  Obhquity  ....  201 

Corrector,  subject  of 230 

Corrector,  effect  of  error  in  . . .231 
Corrector,  use  of  in  ranging  . . .215 
Corrector,  effect  of  error  in  range 

on  237 

Cosine,  Trigonometric  fimction, 

explained 203 

Creeping 261 

Crests,  discussed,  as  to  position  256 

Crimean  War XXVI 

Cromwell,  Ohver XV 

Cross-Fire 119 

Cubic  Measure 19 

Curved  Fire  (Indirect) 119 

Danger  Angle,  discussed  . . . .281 
Danger  Space  and  Angle  of  FaU  . 126 

Data,  Fire 149 

Data,  Fire,  how  secured,  etc.  . . 167 
Dead  Space  discussed  . . . 254, 280 
Dearing,  Capt.,  C.  S.  A.  . . XXIII 

Decimal  Fractions  12 

Decomposition  of  Gun  Cotton  . 84 

Decomposition  of  Nitroglj’cerin  . 88 
Defilade,  mounted,  dismounted 

and  flash 245 

Deflection,  discussion  of  ....  171 


INDEX 


285 


PAGE 


PAGE 


Deflection,  Calculation  of  Formula 

for  173 

Deflection,  the  element  of  ...  167 

Deflection  Difference,  formulas  . 180 

Deflection,  calculation  of  when  no 
A.  P.  examples  of  ...  . 185, 190 

Demolition,  fire  for 153 

Denominate  Numbers 23 

Density  of  Air,  effects  of  ...  . 126 

Density  of  Powder  110 

Departure,  Angle  and  Line  of 

117,  118 

Designation  of  Objectives  . 162, 163 

Detonation 65 

Detonators 93 

Deviations  of  Fire,  Mean  and  Ab- 
solute   152 

Dion  Cassius,  refers  to  use  of 

powder  102 

Directed  Piece,  use  of  as  Aiming 

Point 185 

Direct  Fire  119 

Direct  Fire,  defined 167 

Direct  Fire,  discussion  of  ...  256 

Direction  of  Piece  on  Target,  ex- 
ample of  185 

Dismounted  Defilade 245 

Distant  Range 209 

Distribution  of  Fire,  formulas 

for  181 

Division,  Algebraic 54 

Drift,  discussion  of 132 

Driving-band,  position  of  ...  131 

Drouot,  General  103 

Dummy  and  Dual  Entrench- 
ments   260 

Dust,  visibility  of 266 

Dynamite 90 

Effective  Range 209 

Egyptian  Wars XXVI 

Elevation  121 

Elevation,  Angle  of 118 

Enfilade  Fire 119 

Entrenchments,  character  and 
position  of 259 


Entrenchments,  Dummy  and  Dual 

Visibility  of  260 

Errors  in  Bursting  of  Shrapnel  . 143 

Errors  in  Fuze 143 

Errors  in  Fire 152 

Errors  of  Fire,  practical  results 

of 151 

Equations,  Algebraic  50 

Eugene,  Prince  of  Savoy  . . XXIII 

Explosion 63 

Explosives 61 

Explosive  Compounds  . . . . 65, 81 

Explosive  Gelatin 92 

Explosive  Mixtures 65 

Explosive,  measure  of  potential 

of  109 

Exterior  Ballistics,  scope  of  . . .116 
FaUerica,  a burning  missile  . . . 102 
FaUing  Body,  formula  for  ...  120 
Fictitious  Gun  Problem  of  Major 

McNair 183 

Field  Artillery,  origin  of  ....  100 
Field  Artillery,  classification  of  XXIX 
Field  Guns,  table  of  for  the  year 
1910  . . (see  introductory  part) 

Final  Velocity  119 

Fire  and  Fire  Data 149 

Fire  Data,  what  comprises  . . . 167 
Fire,  Application  of,  discussion 

of  157 

Fire,  Classified  and  Defined,  direct 

and  indirect  167 

Fire,  classified  as  to  elevation  . .119 
Fire,  classified  as  to  direction  . .119 
Fire  Concentration,  formula  for  179 
Fire,  Convergence  of,  formula 

for  181 

Fire,  Continuous,  discussion  of  . 158 
Fire  at  Will,  discussion  of  ...  159 

Fire  for  Demolition  153 

Fire  Control  and  Direction  . . 150 

Fire,  Deviations  of  152 

Fire  at  Single  and  Successive 

Ranges  216 

Fire,  Distribution  of,  formula  for  181 


286 


INDEX 


Fire,  Inaccuracy  of 151 

Fire,  Long-Range,  poor  effect  of  153 
Fire,  Percussion,  discussion  of  . 153 
Fire,  Time,  discussion  of  ...  154 
Fire,  Volley,  discussion  of  ...  158 

Fire,  Sheaf  of 149 

Fire,  Sectors  of 164 

Fire,  Registration  of,  purpose  and 

manner  of 166 

Fire,  Preparation  for  opening  . . 164 

Fire,  Flanking  119 

Fire,  Cross,  Enfilade,  Reverse, 

Direct  119 

Fire,  Indirect  171 

Fire,  Direct  and  Indirect,  Japan- 
ese views  as  to 160 

Fire,  Advantages  of  Indirect  . . 251 
Fire,  positions  for  indirect  . . . 266 
Fire,  objections  to  indirect  . . . 248 
Fire,  masked  and  unmasked  . . 245 
Fire,  against  Infantry,  French 
and  Japanese  systems  ....  346 

Flanking  Fire 119 

Flash  Defilade 245,  265 

Flash,  visibility  of 265 

Forming  the  Sheaf,  how  effected  . 164 

Forrest,  General XV 

Fractions,  Common  and  Decimal  7 
Fragments,  number  of  in  H.  E. 

Shell  145 

Franco-German  War  ....  XXVI 

Franklin,  Battle  of XIX 

Frederick  the  Great,  XIV,  XV,  XXIII 
Frederick  the  Great,  originates 

horse  artillery  104 

Fredericksburg,  concealment  of 

guns  at  255 

French  principles,  acceptance  of 

by  Germans 250 

French  System  of^Fire  against  In- 
fantry   246 

Frustrums 41 

Fulminate  of  Mercury 93 

Fuze,  effects  of  errors  in  . . 143,  144 

Fuze  Setter 230 


FAQE 

Fuze  Setting,  the  element  of  . . 167 

Gelatin,  Explosive  92 

German  ideas  as  to  rapid  fire 

material 250 

Geometrical  Magnitudes  ....  34 

Gettysburg,  concealment  of  guns 

at 255 

Graeco-Turkish  War  . . . XXVII 

Grant,  General  U.  S XV 

Gravimetric  Density  of  Powder  . Ill 

Gravity 98 

Greek  Fire 102 

Gribeauval,  “The  Father  of  Mod- 
ern Artillery” 105 

Guncotton 81,  84 

Guncotton  Powders 90 

Gunnysacks,  use  of  for  cover  . . 261 
Gunpowder,  action  of  in  gun  . . 109 
Gunpowder,  ancient  recipe  for  . 102 
Gunpowder  and  High  Explosives  61 
Gunpowder,  density  and  gra-vi- 

metric  density  of 110 

Gunpowder,  development  of  . . 112 
Gunpowder,  effect  of  on  gun  de- 
sign   112 

Gunpowder,  Ingredients  and  Pro- 
perties of  68,  71 

Gimpowder,  Manufacture  of  . . 69 

Gunpowder,  origin  of 102 

Gunpowders,  Special  73 

Gun,  the  purposes  of,  capacity, 

size,  shape,  etc.  of Ill 

Gustavus  Adolphus  . XXIII, 103, 105 
Gustavas  Adolphus,  “The  Father 

of  Light  Artillerj'”  103 

Hamilton,  General  Sir  Ian,  his 
account  of  the  Battle  of  the 

Yalu  268 

Hand  Measurement  of  Angles  . 200 

Hannibal XV,  XXIII 

Haskell,  Major,  C.  S.  A. . . . XXIII 

Heat  and  Work 109 

Heat,  Mechanical  Equivalent  of  . 110 
Heavy  Field  Artillery  ....  XXXI 
Height  of  Mask,  discussion  of  . 272 


INDEX 


287 


PAGE 


Henderson,  Col.  G.  F.  R.  . XI,  XV 

Hexagonal  Powder  74 

Hood,  General  John  B . . , XVIII 

Horizontal  Deviation 152 

Horse  Artillery XXXI 

Horse  Artillery,  origin  of  ...  . 104 


Howitzers XXXIV 

Howitzers,  origin  of 106 

High- Angle  Fire  119 

High  Explosive  Shell  (H.  E.  Shell), 

description  of 145 

High  Explosive  Shell,  number  of 

fragments  of 145 

High  Explosive  Shell,  secret  com- 
pound used  in  146 

High  Explosive  Shrapnel  (Single 

Type  Ammunition) 144 

High  Explosives  61 

Inaccuracy  of  Fire  151 

Indian  Mutiny 20 

Indirect  Fire  and  Deflection  . . 171 

Indirect  Fire,  defined 167 

Indirect  Fire,  discussion  of  as  to 
employment  and  objections  . . 248 
Indirect  Fire,  positions  for  ...  266 
Infantry,  manner  of  attack  . 161,  246 
Infantry,  assistance  of  by  Artil- 
lery   165 

Initial  Velocity 119 

Interior  Ballistics,  defined,  scope 

of 108 

Jackson,  General  T.  J.  (Stonewall) 

XVIII,  XIX 

Japanese  Methods  of  Conceal- 
ment   267 

Japanese  experience  as  to  masks  246 

Japanese  Equipment  in  Man- 
churia   255 

Japanese  views  as  to  kind  of  Are  to 
be  employed  against  Infantry  . 160 

Japan-China  War  ....  XXVII 

Jump,  explained  117 

Kuropatkin XXI 

Langlois,  General,  “Father  of  Mod- 
ern Rapid  Fire  Material”  . . XIV 


PAGE 

Latimer,  Capt.,  C.  S.  A.  . . . XXIII 
Laying,  discussion  of  direct  and 

indirect  248 

Lee,  General  Robert  E.  . XII,  XV 

Light  Artillery XXX 

Light  Artillery,  origin  of  ...  . 102 

Light  Howitzers XXXIII 

Line  of  Departure 117 

Line  of  Fire  117 

Line  of  Sight 117 

Long  Measure  17 

Long  Range 209 

Long,  General,  C.  S.  A.  . . XXIII 
Louis  XIV,  founds  Artillery 

Schools  103 

Macomb,  General XX 

Macedonian  Wars,  authorities  on  XXV 
Magnitudes,  Geometrical  ....  34 

Mahan,  Capt.  A.  T XVI 

Manchurian  War XXVII 

Manufacture  of  Gunpowder  . . 69 

Manufacture  of  Hexagonal  Pow- 
der   74 

Manufacture  of  Smokeless  Pow- 
der   79 

Manufacture  of  Guncotton  ...  82 

Manufacture  of  Nitroglycerin  . 85 

Marcus  Graccus,  his  recipe  for 

gimpowder  102 

Marlborough,  Duke  of  . . XV,  104 
Martinet,  General,  Father  of  Rigi- 
dity and  Discipline 105 

Mask,  discussion  of 245 

Mask,  practicability  of  ....  246 
Mask,  improper  use  of  by  Japan- 
ese and  Russians 153 

Mask,  Clearing  the 269 

Mask,  Clearing,  formula  for  . . 123 
Mask,  Percin’s  Rule,  for  clearina  276 
Mask,  Miles’  Method,  for  clearing  277 
Mask,  table  showing  height  of  . 274 

Masked  Positions 245 

Masked  Fire 245 

Material,  visibility  of 263 

Mathematical  Signs 3 


288 


INDEX 


PAGE 

Maximum  Effective  Range  . . . 209 
Maximum  Ordinate,  defined,  posi- 
tion of  126 

McDougaU XVI 

McMahon,  an  article  by,  concern- 
ing the  Mask 248 

McNair  Major,  His  Fictitious 

Gun  Problem 183 

Mean  Deviation  of  Fire  . . . .153 

Mean  Point  of  Burst  232 

Measurement,  Angular  ....  193 

Measures,  tables  of 17 

Mechanical  Equivalent  of  Heat  110 

Mensuration 43 

Mercury  Fulminate 93 

Metric  System 19 

Mil,  Derivation  and  origin  of, 

value  of 168 

Mils,  relative  value  of  in  yards  . 169 
Miles’  Method,  clearing  mask  . . 277 

Military  Crest 256 

Mitrailleuse,  origin  and  use  of  . 106 
Moses,  references  during  time  of, 

to  powder 102 

Motion,  of  projectile  119 

Motion  of  Projectile  in  Vacuum 

and  in  Air  120,124 

Mountain  Artillery XXIX 

Mounted  defilade 245 

Mowbray  Process  85,  87 

Multiplication,  Algebraic  ...  54 

Napier,  Sir  Charles  ....  XXIII 
Napoleon,  XV,  XVI,  XVII,  XVIII, 

101, 103 

Napoleon,  his  improvements  in 

artillery 105 

Napoleon  (Smooth  bores)  . . . 106 

Napoleonic  Wars XXV 

Narses XII 

Nelson  XII,  XV,  XVI 

Neuffer,  Lieutenant  WiUiam,  his 
remarks  on  artillery  practice  in 

Manchuria  153 

Nile,  Battle  of XVI 

Nimrod XII 


PAGE 

Nitroglycerin  ...  81,  85,  87,  88 

Normal  Burst,  Height  of  ...  231 

Normal  Corrector  234 

Objectives,  Designation  of  . 162,  163 

Obhque  Eire 119 

Obhquity,  explained,  corrections 

for  201 

Observation  of  Fire,  in  general  . 239 
Observation  of  Terrain  ....  164 
Observation,  Sectors  of  ....  164 
Observation  for  Range  . . .211,  212 
Observation,  with  one  observer  . 242 
Observation,  with  two  observers  242 

Observing  Bursts 232 

Onager,  form  of  ballista  ....  102 

Onosander XIV 

Parallax,  Angle  of,  explained  . . 175 
Parallax  Method,  explained  173,  174 
Parallax  Method,  examples  un- 
der   176,  177 

Parallax  Table 205 

Parallax,  Corrected  for  Obli- 
quity   205 

Parliamentary  War XXV 

Pegram,  Col.,  C.  S.  A.  . . XXIII 
Pelham,  Major,  C.  S.  A.  . XXIII 
Pendleton,  General,  C.  S.  A.  XXIII 
Peninsula  of  Virginia  ....  XVIII 

Percentage  29 

Percin’s  Rule,  for  clearing  mask  . 276 
Percussion  Fire,  discussion  of  .153 

Philip  of  Macedon  101 

Philippine  War XXVII 

Philostratus,  refers  to  powder  . 102 

Pitching  of  Projectile 125 

Plane  of  Fire  and  Departure  . . 117 
Plotter,  explained  ....  193,  194 
Plutarch,  refers  to  powder  . . . 102 
Poague,  Col.,  C.  S.  A.  . . . XXIII 
Point  of  Fall  or  Impact  . . . .118 

Point  of  ignition  62 

Pons  Asinorum,  rule  of  ....  170 

Position,  Angle  of 118 

Position  and  the  Mask  ....  245 
Position,  Discussion  of 256 


INDEX 


289 


Positions  for  Entrenchments  . . 259 
Positions  for  clearing  the  mask  . 270 
Powder,  that  is  quick  for  the  gim  . 112 
Powder,  that  is  slow  for  the 

gim 112 

Powders,  special  73 

Powders,  Prismatic 75 

Powders,  Smokeless 77 

Powders,  Guncotton 91 

Powders  ....  (See  gimpowder) 

Powers  and  Roots 31 

Practical  Gunnery,  sub-divisions 

of  148 

Preparation  of  Fire,  manner  of  . 164 
Pressure  Curves,  illustrated  . . 114 

Prism,  what  it  is 220 

Prismatic  Powders  75 

Prisms  of  the  Weldon  Range 

Finder  221 

Projectile,  unimpeded  motion  of  119 
Projectile,  motion  of  in  vacuum 

and  in  air 120,  124 

Projectile,  Taper  base  shell  . . 125 
Projectile,  steadiness  of  in  flight  125 
Projectile,  shape  of  head  of  . . . 124 
Projectile,  smoothness  of  ...  125 
Projectiles,  Elongated,  advantages 

of  130 

Projectiles,  weight  of  shell  and 

shrapnel 146 

Projectiles  . (see  shrapnel  and  shell) 

Proportion  26 

Pimic  Wars  XXV 

Pyramids  40 

Quadrant  Angle  of  Departure  . . 118 

Quadrilaterals  38 

Rafales,  use  of 155 

Raking  Fire  119 

Range  and  Ranging  209 

Ranges,  Classified 209 

Range,  the  element  of 167 

Range  of  trajectory  117 

Range,  greatest  possible,  defined  . 129 
Range,  Maximum  effective,  and  of 
maximum  effect  209 


PAOB 


Range,  determination  of  by  sound  210 


Range,  Adjustment  of  ....  210 
Range,  determined  by  bracket- 
ing   210,  211 

Range,  Observations,  etc.  . 211,  212 
Range,  correction  of  by  correc- 
tor   215 


Range  Finder,  Weldon,  explained  217 
Range,  Long,  poor  effect  of  fire 


at  153 

Ranges,  single  and  successive  . 216 
Ranging  by  trial  shots,  etc.  .211,212 

Ratio  and  Proportion 26 

Rawlinson XII 

Rear  Crest  256 

Remaining  Velocity 118 

Reflection,  effect  and  explanation 

of  ‘ 217 

Reflection,  angle  of 218 

Refraction,  explanation  of  . . . 218 
Registration  of  Fire,  purpose  and 

manner  of 166 

Registration  Marks,  discussion  of  157 

Reverse  Fire 119 

Ricochet  of  Shrapnel  144 

Rifling,  origin  of  106 

Rifling,  purpose  and  effect  of  129,  130 
Rifling,  effect  on  motion  . . 125,  126 
Right  Angle,  number  of  mils  in  . 168 
Rigidity  of  Trajectory  ....  123 

Roberts,  Lord  XIV 

Roots  (square  root) 31 

Rotation,  secured  by  rifling,  pur- 
pose of  129 

Ruchel  XIII 


Ruler,  Battery  Commander’s,  ex- 
plained   198 

Russian  methods  of  concealment  267 
Russian  dummy  entrenchments  . 260 
Russo-Japanese  War  . . . XXVII 

Russo-Turkish  War XXVI 

Salvos,  searching  by  155 

Salvos,  Verifying,  discussion  of  . 157 
Schwartz,  not  inventor  of  gun- 
powder   102 


290 


INDEX 


PAGE 

Scorpio,  form  of  catapult  ...  102 

Screens,  use  of 245 

Screens,  concealment  by  ...  . 266 
Searching  areas  by  fire,  discussion 


of  

154,  155,  156 

Searching  by  Volleys  and  Salvos  155 

Seaton,  Lord  .... 

XVII,  XVIII 

Secret  Compound  used 

in  H.  E. 

SheU  

146 

Sectors  of  Fire  . . . , 

164 

Sectors  of  Observation 

....  164 

Sedan 

. . . . XIX 

Senarmont,  General 

103 

Seven  Weeks’  War 

. . . .XXVI 

Seven  Years’  War 

. . . .XXVI 

Shape  of  Head  of  Projectile  . . 124 

Sheaf  of  Fire 149 

Sheaf,  opening  of,  conditions  of  . 165 
Sheaf,  Formation  of,  how  effec- 
ted   164 

Shell,  High  Explosive,  description 

of  145 

Shell,  H.  E.  weight  of 146 

Shell,  H.  E.  number  of  fragments 

of  145 

Shell  Fired  Vertically,  formula  for  121 

Shenandoah  Valley XVIII 

Sherman,  General XV 

Shrapnel,  description  of  ....  138 
Shrapnel,  burst,  cone,  velocity, 
zone,  interval  of  burst  138,  139,  140 
Shrapnel,  High  Explosive  (Single 

type  ammunition) 144 

Shrapnel,  weight  of 142 

Shrapnel,  invented  by  Major 

Shrapnel 105 

Siege  Artillery  XXXIV 

Sights,  of  pieces,  as  aiming  points 

185,  186 

Simple  Equations  50 

Sine,  Trigonometric  function,  ex- 
plained   203 

Single  Type  Ammunition  . . . 144 
Site,  Angle  of,  explained  ....  224 
Skirmishers,  Japanese,  advance  of  246 


Slope  of  Descent  of  shell  and 

shrapnel 258,  259,  266 

Smoke,  visibihty  of 265 

Smokeless  Powders 77 

Smokeless  Powders,  properties  of  80 
Smooth-bore  guns  (Napoleons)  . 106 

Solids 39 

South  African  War XXVII 

Spanish  American  War  . . XXVII 

Special  Powders  73 

Spheres  42 

Spin,  Persistence  of  and  reason 

of 133 

Spring  Hill,  Battle  of  . . . XVIII 
Stationary  Target,  attack  of  155,  156 
Steadying  Band,  Forward  . . . 132 
Straight  Angle,  number  of  mils  in  168 

Striking  Angle 118 

Study,  Value  and  necessity  of  . XI 

St.  Vincent,  Battle  of XI 

Subtraction,  Algebraic  ....  53 

Supporters  of  Combustion  ...  61 

Surfaces 37 

Suvaroff,  or  Suwarrow,  exponent 

of  the  bayonet  105 

Tangent,  explained 168 

Tangent,  Trigonometric  function, 

explained  203 

Taper-Base  Shell 125 

Targets,  designation  of  ....  164 
Taylor,  General  “Dick”  ....  XII 
Telescope,  B.  C.,  used  as  Aiming 

Point 190,  191 

Temperature,  effects  of  ....  126 
Terrain,  Observation  of  ....  164 
Tests,  Experimental,  of  Shrapnel,  142 

Thawing  Dynamite 92 

Thawing  Nitroglycerin  ....  88 

Theory,  value  of  XI 

Thermal  Unit  HO 

Thirty  Years’  War  XXV 

Time  Fire 154 

Timur  XIV 

Torstenson,  General  103 

Trafalgar,  Battle  of XII 


INDEX 


291 


Trajection 101 

Trajectory,  an  analytical  curve  . 116 
Trajectory,  elements  of  ....  117 
Trajectory,  Rigidity  of  ....  123 
Trajectory,  Height  of,  formula  for,  123 
(see  also  Clearing  the  Mask) 
Trajectory,  Flatness  of  affects  dan- 
ger space  and  angle  of  fall  . . 126 
Trees,  transplanted,  used  as  screens  267 

Triangles  38 

Trigonometric  fimctions  explained  203 

Turenne,  Marshal XXIII 

Turkish  Wars  . . XXVI,  XXVII 
Twist  of  Rifling,  effect  of  motion 

125,  126,  130 

Twist,  Uniform  and  Increasing  . 131 

Twist,  Minimum 131 

Tyndall XII 

Uniforms,  visibihty  of 263 

Unmasked  Positions  245 

Velocity  of  Sound,  formula  for  . . 210 
Velocity,  High,  affects  danger 
space,  trajectory,  angle  of  fall  . 128 
Velocity  of  Emission  of  powder  . 110 

Velocity  of  Projectile 118 

Velocity,  Final 119 

Velocity,  Initial  or  Muzzle  . . . 119 
Velocity,  Remaining 119 


Verifying  Salvos,  discussion  of  . 157 

Vertical  Angles 169 

Vertical  Deviation  of  Fire  . . . 152 

Virtual  Images 220 

Visibihty,  discussed 262 

Volley  Fire,  discussion  of  ...  158 

Volleys,  searching  by 155 

Volumes  48 

Volume,  Measure  of  19 

Von  der  Goltz  .XIII,  XIV,  XV,  XIX 

VonMoltke  XV,  XIX 

Walker,  General  R.  Lindsay, 

C.  S.  A XXIII 

Weight,  table  of 21 

Weldon  Range  Finder,  explained  217 
Wellington,  Duke  of  ...  . XI,  XV 
Wolseley,  Field  Marshal  Lord 

XIV,  XXII 

Work  and  Heat  109 

Yalu,  Battle  of,  the  losses  of 
Russian  Artillery  at  ....  251 
Yalu,  Battle  of,  concealment  of 
Japanese  and  Russian  Guns  at . 867 
Yards,  relative  value  of  in  mils  . 169 

Zahnski  Torpedo 125 

Zone,  effective,  of  Shrapnel  . . . 140 
Zone  Fire,  discussion  of  use  of  . 155 
Zone  Fire,  adaptation  of  ...  . 159 


Date  Due 

f 

2 % 

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i/lR?  7 ’t? 

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5 1?813 


2503  78 


